Instant Runoff Voting with Resticted Ballots

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Instant runoff voting with restricted voting

AuthorGary W. Cox, Professor ofPolitical Science, University of California, San Diego. B.S.with honors, History, California Institute of Technology, 1978. Ph.D., Social Science,California Institute ofTechnology, 1982. Fellow, American Academy of Arts andSciences. Former Guggenheim Foundation Fellow. Curriculum vitae attached.

I am the author of over thirty articles in scholarly journals analyzing different electoralsystems around the world and ofMaking Votes Count: Strategic Coordination in theWorld's Electoral Systems (winner of the American Political Science Association'spremier prize, the Woodrow Wilson Foundation Award). I have also lectured extensivelyat universities in the U.S. and abroad on electoral system design. Most of my workfocuses on how different voting procedures affect voters' and candidates' strategies andbehavior. Among the voting procedures which I have examined are the standard pluralityvoting system and various alternatives to it, such as approval voting, the single non­transferable vote, cumulative voting, majority run-off, and a wide variety of ranked­preference voting methods (including the alternative vote, also known as instant runoffvoting, or IRV for short).

DateMay 22,2003.

Executive SummaryI was asked to review San Francisco's proposed instant runoff voting (IRV) system,which is slated for its initial use in the November, 2003, municipal election. In myreview, I focus on several ways in which San Francisco's version ofIRV differs fromother ranked-choice voting systems and the implications of those differences. Myobservations and conclusions follow.

The San Francisco sy'stem is unusual among IRV and IRV-like systems in both thephysical layout of the ballot and in that it restricts voters to ranking only three candidateson the ballot, rather than allowing them to rank as many as they wish. 1 It is uniqueamong current IRV and IRV-like systems in that it allows the chief election administratorto decide whether and how much to restrict voters' rankings.2

This document makes three main points. First, the ranking restriction can change theelection outcome from what it would have been, had voters been allowed to rank as manycandidates as they wished. Second, the discretion granted under law to San Francisco'sDirector of Elections, allowing him or her to decide whether and how much to restrict

I. The only other current systems of which I am aware that are similar to IRV and restrict voters' rankingsare those used to elect the Mayor of London and the President of Sri Lanka.2. To the best of my knowledge, no previous IRV or IRV-like system has allowed the chief electionadministrator to decide whether and how much to restrict voters' rankings.

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voters' rankings, gives that officer the ability to affect the outcome of the election. Third,the ballot format proposed for San Francisco is more confusing for voters than the formatadopted virtually everywhere else that IRV has been used.

How restricting the number of rankings can affect the outcomeRestricting the number of rankings voters can express on the ballot can change theelection outcome from what it would have been, had voters been allowed to rank as manycandidates as they wished. Indeed, restricting voters' options will change the electionoutcome whenever such restrictions prevent what would otherwise be "late transfers"from affecting the outcome. Before explaining what "late transfers" are, I first provide anexample of how restricting voters' rankings can change the outcome (Example 1) andthen briefly explain how the San Francisco system diverges from true IRV systems.

Example 1In this example, there are five candidates, denoted with capital letters: A, B, C, D, and E.Each voter or bloc of voters ranks these five candidates in some order of preference. Forexample, a voter who ranks the candidates DBCAE most prefers candidate D, ranks Bsecond, and so on. If a voter has clear preferences regarding A and B but no preferenceregarding C, D and E, then this voter's preference ranking would be written AB or BA(depending on which of the ranked candidates was judged best).

NUMBER OF VOTERS IN BLOC HOW VOTERS IN THIS BLOC RANKTHE CANDIDATES

8,000 ABC9,000 BA3,500 CDEAB2,000 DECAB1,000 EDCAB

In this example, there are 17,000 voters (in the first two rows) who split between the twomajor candidates, A and B (their votes go to A and B in the first round and there is noneed for transfers). Ip addition, there are 6,500 (= 3,500 + 2,000 + 1,000) voters whosevotes will transfer to one of the top two candidates late-after the minor candidates C, Dand E have been eliminated.

If the election is held under IRV with no restriction on voters' rankings, and if each votervotes sincerely, then the actual rankings put on the ballots will correspond to thepreference rankings in the table above.3 The outcome will be a victory for candidate A.(In the first round, candidate E is eliminated and her votes redistributed, all to D. In the

3. A voter votes sincerely if s/he votes first for her/his favorite candidate, second for herlhis second-mostfavorite candidate, and so on, in order of true preference.

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second round, candidate D is eliminated and his votes redistributed, all to C. In the thirdround, candidate C is eliminated and her votes redistributed, all to A.4)

Ifthe election is held under IRV with each voter restricted to ranking only threecandidates, and if each voter votes sincerely, then the actual rankings put on the ballotswill be as in the following table:

NUMBER OF VOTERS IN BLOC HOW VOTERS IN THIS BLOC RANKTHE CANDIDATES

8,000 ABC9,000 BA3,500 CDE2,000 DEC1,000 EDC

The outcome in this case is that candidate B wins. The reason is that, after candidate C iseliminated in the third round, there is no information on the ballot regarding how the late­transfer voters rank the two main candidates. Thus, the 6,500 votes simply extinguishafter the third round, and candidate B wins with 9,000 votes to A's 8,000.

By restricting the expression of preference on the ballot, a burden is imposed on voterswhose votes would transfer late. They must anticipate the extinguishment of their votesand vote strategically, moving candidate A up to at least third place in their expressedrankings. If the late-transfer voters do not possess the information necessary to anticipatetheir predicament, their votes will be wasted in the sense that the election outcome endsup being what it would have been had they all abstained. This burden-of anticipating arelatively long chain of calculations accurately; and voting strategically in order to ensureone's vote does influence the ultimate outcome-falls only on the late-transfer voters, noton the early-transfer voters.

Note that, in this example, only 6,500 of the 23,500 voters (28%) would wish to rankmore than three candidates on the ballot. Obviously, this number (and percentage) couldvary, with different crssumptions about the sizes of the voting blocs. Note also that thewinner under restricted IRV (i.e., B) wins despite the fact that 14,500 of23,500 voters(62%) prefer A to B. Put another way, the winner under restricted IRV, B, has thesupport of only 38% of the voters. This percentage could vary, with differentassumptions about the sizes of the voting blocs.

Traditional run-off, IRV and restricted IRVAs Reilly and Maley note, among advocates ofIRV, "it has regularly been stressed thatvoters should be able to choose how many preferences they will indicate."s To see why

4. The simple pattern of transfers, in which all E's votes transfer to D, and so on, is for ease of expositiononly. The essential features of the example are that: (1) there are voters who rank C, D, and E, in someorder, in the fIrst three spots on their ballots; and (2) these voters are more likely to rank A fourth than B.

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electoral reformers generally do not endorse restricted IRV, such as San Francisco'sproposed system, let's compare it to a traditional run-off.

In the latter system, the two candidates who garner the most votes in the first round ofvoting meet again some weeks later in a run-off election. All voters know who the twofinalists are and can vote for whichever they prefer.

In contrast, under an IRV system in which voters can rank at most three candidates,voters must correctly anticipate who the top two candidates will be in the final round ofvote-counting of the IRV process, and then vote for one of them. If they fail to correctlyanticipate who the top two candidates will be, they will end up casting what they maythink of as a "run-off' vote for a candidate who does not in fact make it to the finalround. Thus, under a restricted IRV system, some voters who would have had theopportunity to participate in the run-off under a traditional system are effectivelydebarred from participating in the "run-off' under IRV.6

As an example, consider the first-round results from the 1999 mayoral election in SanFrancisco: Willie Brown 39%; Tom Ammiano 25%; Frank Jordan 17%; Clint Reilly13%; scattered 6%. Suppose this election had been held under the proposed version ofIRV. Consider a voter who preferred at least three other candidates to both Brown andAmmiano. Such a voter might mistakenly have believed that the top two finishers wouldbe Brown and Jordan. Acting on this understandable belief (Jordan had formerly servedas Mayor of San Francisco), the voter might have ranked Jordan at least third, in anattempt to avoid wasting their vote. However, their effort would have gone for naught, asin fact Jordan was not one of the top two finalists. The voter's ballot would thereforehave extinguished before affecting the real race (between Brown and Ammiano).

Note that IRV, in which voters are allowed to rank as many candidates as they wish,solves the "guessing" problem just noted. Any voters who wish to ensure that their voteswill count in every stage of the process about which they care simply have to rank all thecandidates about whom they care. If they truly do not care about the serious candidatesmost likely to last into the later rounds, then they can voluntarily withdraw from theprocess. If they do h~ve preferences among the serious candidates, and are allowed torank as many as they wish, then their votes will always count. But if they have apreference but the ballot only allows three rankings, they may be involuntarily removedfrom the set of voters whose votes count in the later and more crucial rounds.

Both true IRV (in which voters are allowed to rank as many as they wish) and traditionalrun-off systems seek to ensure that the candidate ultimately elected has the support of amajority of all voters. They do this by conducting one or more run-off elections, either in

5. Reilly, Benjamin, and Michael Maley. 2000. "The Single Transferable Vote and the Alternative VoteCompared." In Elections in Australia, Ireland and Malta Under the Single Transferable Vote, ed. ShaunBowler and Bernard Grofman. Ann Arbor: University of Michigan Press, p. 43.6. The Electoral Reform Society's web site also notes this feature in connection with the method used toelect the Mayor of London (www.electoral-refom1.org.ukJpublications/leaflets/london.htm. accessed May8,2003).

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the traditional sense of holding a separate election some weeks later or in the sense ofusing voters' rankings to hold the run-off "instantiy." In restricted IRV, however, somevoters may unwittingly remove themselves from participating in the run-off, simply byvirtue of guessing wrong. Thus, a core value of the whole IRV system-that of ensuringthe election of a candidate with majority support among all voters who wish toparticipate-is violated (as Example 1 showed).

Defining early- and late-transfer votesHaving provided an example ofhow restricted IRV can go wrong and contrasted it to twomore common systems-traditional run-off and unrestricted IRV-I turn now to a moretechnical discussion of the situations under which restricting voters' rankings will affectthe outcome. This returns the discussion to the issue of early and late transfers.?

To explain what early and late transfers are, consider a race in which there is no majoritywinner until all but two candidates are eliminated. In an unrestricted IRV election, thefinal vote for the ultimate winner can be divided into two mutually exclusive categories:(1) the early-transfer vote, defined as the number of votes that come from ballots rankingthe ultimate winner first, second or third; and (2) the late-transfer vote, defined as thenumber of votes that come from ballots ranking the ultimate winner fourth or lower.Restricting voters to three rankings prevents what would otherwise be the late-transfervote from being counted, if voters mark their ballots the same way in both theunrestricted and the restricted election. If some voters do figure out that they shouldchange the way they mark their ballots in the restricted election, it is still the case that notall of the late-transfer votes will be counted, unless every late-transfer voter correctlyanticipates who the two leading candidates after the third round will be and ranks one ofthem in the top three on the ballot. Failure to count the late-transfer vote fully, however,will alter the election outcome whenever the late-transfer vote differs "enough" from theearly-transfer vote.

To clarify what is "enough," consider an election in which voters are not restricted andsuppose that the first-place candidate gets E1 early-transfer votes ("E" for "early" and"1" for the "first-place" candidate) and L1late-transfer votes in the final round.Meanwhile, the secopd-place candidate gets E2 early-transfer votes ("2" for the "second­place" candidate) and L2 late-transfer votes in the final round. Since the first-placecandidate by definition wins, we know that E1 + L1 > E2 + L2 (that is, the ultimatewinner gets more votes than the ultimate runner-up, in the final count). Restricting votersto three rankings can change the election outcome whenever E1 < E2. In other words, theelection outcome can be changed whenever the second-place candidate has a lead amongthe early-transfer voters (those ranking at least one of the top two candidates in the first

7. In this section, I consider the conditions under which restricting voters to three rankings can change theoutcome. Restricting voters to n rankings can also change the outcome, whenever n is less than one lessthan the number of candidates.

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three ranks on the ballot) but trails when the late-transfer voters (all the rest) are alsocounted. 8

The late- and early-transfer votes are likely to differ whenever one side of the left-rightpolitical spectrum is more divided, in the sense of fielding more candidates and splittingits vote more widely, than the other. Suppose, for example, that there are 10 leftistcandidates for mayor but only 3 centrist and right-of-center candidates. The "real" race isbetween leftist candidate A and centrist candidate B. The centrist and right-wing voteswill transfer to B early, as there are only three candidates from the center and right on theballot. Thus, the vast bulk of the late-transfer vote will come from leftist voters. Iftheearly-transfer vote gives a close victory to the centrist, but counting all votes would electthe leftist, then preventing the late-transfer vote from being counted will change theoutcome.

Example 2An example illustrating how restricting voters to three rankings can change the electionoutcome when one side of the political spectrum is more divided than the other is basedon the 1999 race for District Attorney in San Francisco. This race featured fivecandidates in the first round of what was then a traditional run-off process: Gonzalez,Castleman, Hallinan, Fazio, and Schaeffer. The vote totals in the first round were 20,153for Gonzalez, 17,677 for Castleman, 68,424 for Hallinan, 67,145 for Fazio, and 5,614 forSchaeffer (for a total of 179,013 ballots). In the run-off election, Hallinan beat Fazio by1,820 votes.9

What if San Francisco had used IRV with voters restricted to three rankings in 1999?Could the outcome have changed? The answer is "yes."

To see how, suppose that 5,000 voters ranked Gonzalez, Castleman and Schaeffer, insome order, in the top three places on the ballot. This would represent only 2.79% of thetotal 179,013 ballots cast. Suppose further that, if given the opportunity, 70% ofthesevoters would have ranked Hallinan fourth, while 30% would have ranked Fazio fourth.(This figure seems plausible, given that both Gonzalez and Castleman were to the leftpolitically ofHallinap., with Fazio to the right. Thus, voters who ranked both thesecandidates in their top three would be considerably more likely to rank Hallinan aboveFazio than the reverse.) Suppose finally that, had the election been held under anunrestricted IRV procedure, Hallinan would have beat Fazio by the same margin that hedid in the actual run-off (viz., 1,820 votes). Given these three assumptions, restrictedIRV would have elected Fazio, not Hallinan. The reason is that, under restricted IRV, the5,000 ballots ranking neither Hallinan nor Fazio in the top three would extinguish,depriving Hallinan of 5,000x.7 = 3,500 votes and depriving Fazio of 5,000x.3 = 1,500

8. We say "can" change the outcome, rather than "will," only because it is possible that late-transfer voterswill anticipate the extinguishment of their ballots under restricted IRV and take effective action to avoidthat outcome. As explained above, however, correct anticipation may be difficult.9. For the data on the S.F. District Attorney's race: http://www.sfgov.org/site/election page.asp?id=5877,accessed May 9,2003.

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votes. Relative to Hallinan, then, Fazio gains 2,000 votes, which is sufficient toovercome the vote margin by which he lost (1,820).

Obviously, other assumptions can also generate this outcome. For example, if 10,000ballots ranked Gonzalez, Castleman and Schaeffer, in some order, in the top three placeson the ballot; and 60% of them would have ranked Hallinan fourth while 40% wouldhave ranked Fazio fourth; then again restricted IRV would have elected Fazio, rather thanHallinan.

How likely is it that restricting the number of rankings mightaffect the outcome?How likely is it in practice that the election outcome in an IRV election will be changedby restricting voters to three rankings? One way to shed light on this question is bylooking at the Australian experience with IRV. The Australians have used IRV inelections to their federal House ofRepresentatives since 1919 and they sometimes reportelection results in a way that allows one to see the vote counts at each stage of theprocess-the initial count, the second count (after some candidate has been eliminatedand his/her votes distributed), and so on to the final count. 10 In some cases, theinformation provided conclusively shows that the winner of the election would have won,even had voters been restricted to three rankings. In other cases, the possibility remainsthat the election outcome would be changed by restricting voters to three rankings.

When the ranking restriction will not affect the outcomeLet's consider first the situations in which the outcome would not change. The simplestsuch case is one in which a particular candidate wins an outright majority of first­preference votes and is therefore elected at the first count. Restricting voters' rankings insuch situations will not affect the outcome, as the first-place rankings alone suffice todetermine the outcome.

Other cases in which there would be no change in outcome involve very strongcandidates who win by a lot but not necessarily at the first round. An example is theBarton, NSW district in the 10 November 2001 elections. The results from this electionare displayed in Appendix 1. As can be seen, the ultimate winner, Robert McClelland,has 35,871 votes in the first count. This exceeds the total number of votes garnered bythe second-place candidate in the final round of voting (viz., 32,873). Thus, even if theelection had been re-counted, with only voters' first three preferences allowed into thecount, McClelland would have won by at least 35,871-32,873 = 2,998 votes. In fact, itcan be deduced that he would have won by considerably more than this sum but all thatmatters for present purposes is that restricting voters' options in this particular race wouldnot have affected the outcome.

10. I accessed Australian data for their 2001 election from psephos.adam-carr.net/psehpos/index47.htrnl, onMay 1, 2003, and May 20,2003.

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When the ranking restriction could affect the outcomeCases in which the outcome could be affected by adopting San Francisco's three-rankingrestriction are those in which the ultimate winner's vote at the end of the third count issmaller than the ultimate second-place finisher's final total (and voters vote sincerely).To explain why this condition works, recall that, ifthe ultimate winner gets fewer early­transfer votes than the ultimate runner-up (i.e., E1 < E2), then the three-rankingrestriction will change the outcome. This is because the three-ranking restrictioneffectively prevents the late-transfer votes from being put on the ballot and, hence,prevents them from being counted.

To identify cases in which the outcome could be changed, then, we need to identifyelection outcomes in which it is possible that E1 < E2. As shown in Appendix 3, E1must be at least as great as the ultimate winner's vote at the third count and no greaterthan his/her vote at the final count. Similarly, E2 must be at least as great as the ultimaterunner-up's vote at the third count and no greater than hislher vote at the final count.Thus, it is possible that E1 < E2 whenever the ultimate winner's third-count vote total(the smallest E1 could be) is less than the ultimate runner-up's final vote total (the largestE2 could be).

As an example consider the results from Adelaide, South Australia, in the 10 November2001 elections, displayed in Appendix 2. There were a total of77,513 valid ballots castin this election, of which 34,258 ranked the ultimate winner, Worth, first; while another28,732 ranked the ultimate second-place finisher, Stanley, first. Thus, there were 77,513- 34,258 - 28,732 = 14,523 ballots that we know did not rank either of the top twocandidates first. In the second round, Worth and Stanley garnered an additional 598 and457 votes, respectively, from voters who had ranked Peacock first. These ballots thusclearly rank at least one of the top two candidates in second place. In the third round,Worth and Stanley garnered an additional 519 and 1,635 votes, respectively, from voterswho had ranked Osborn first (or had ranked Peacock first and Osborn second). Theseballots thus clearly rank at least one of the top two candidates somewhere in the top threeplaces.

Are there any other ballots from Adelaide that we can be sure ranked at least one of thetop two candidates in one of the top three places? As it turns out, no. All the othertransfers to these candidates could result from information contained in the fourth- andfifth-place rankings. In particular, the 11,314 votes that transfer from Mann in the finalcount could all come from ballots that rank Mann, Osborn and Peacock (in some order) inthe first three places. There is nothing in the election results that allows us conclusivelyto discount this possibility.

Since we do not have access to the actual ballots cast in Adelaide, the most we can sayabout the number of early-transfer votes that Worth gets is that it is at least his third­round total (of35,375) and at most his final-round total (of38,928). Similarly, we knowthat Stanley's early-transfer vote total, E2, lies somewhere between 30,824 and 38,585.It is thus quite possible, given the published election summary, that E1 < E2, in whichcase imposing a three-ranking restriction on voters could have changed the outcome.

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How many of the Australian outcomes could possibly have been changed, had the ballotsrestricted voters to three rankings? That is, how many are such that the ultimate winner'sthird-round total falls short of the ultimate runner-up's final-round total? In theNovember 2001 elections, there were 32 such cases, out of 150 total districts. Thus,21.3% of the election outcomes could conceivably have been changed, had theAustralians used the proposed S.F. restriction on voters' rankings.

There are two considerations that make this figure loom larger in San Francisco. First,note that the likelihood of the election outcome being changed is greatest in the mostclosely contested elections, in which the perceived fairness of the electoral process ismost crucial. Second, note that all of the Australian constituencies are substantiallysmaller in population than is the City of San Francisco, with about 70,000 to 85,000 votescast as opposed to over 200,000 in the 1999 mayoral election. They are also substantiallyless diverse. Both the size and diversity of the S.F. electorate, compared to the Australianelectorates, suggest that the chances of large fields of candidates splitting the vote finelyare greater in S.F., which in tum raises the probability that vote restrictions would affectthe outcome.

How discretion in deciding whether to restrict the number ofrankings can affect the outcomeThe previous sections have illustrated the conditions under which restricting the numberof rankings voters are allowed to express on the ballot can affect the outcome of theelection. This section notes that, because the San Francisco Charter grants discretion tothe Director of Elections in determining whether and how much to restrict voters'options, it opens the door to potential manipulation of election outcomes.

Suppose that the next mayoral race in San Francisco features two main candidates, onemore liberal (L), one more conservative (C), along with a smattering of minor leftistcandidates (A, B, C, D and E). The race, let us say, is relatively close between the toptwo contenders, Land C. Moreover, suppose also that (1) many of the minor leftist voteswould transfer between the minor leftist candidates at least three times before reaching amajor candidate, if the minor leftist supporters simply rank candidates on the ballot inorder of their true preferences; and (2) a substantial majority of the minor leftist votersprefer L to C. If the incumbent Director of Elections becomes aware of these features ofthe election-and we shall argue that he is in an excellent position to do so-then hefaces a moral temptation, as he could have a clear political incentive either to limit or notto limit.

If the Director favors C, then his political goal (electing C) is best served by imposing thestrictest allowable limit on voters' options. This imposes a burden on leftist leaders, whomust reach their voters and convince as many as possible that they should rank L at leastthird, even if their true preferences would dictate otherwise. To the extent that leadersare unsuccessful in reaching all leftist voters with this message (and convincing them), acertain number of leftist voters will cast ballots that exhaust before they transfer to eitherL or C, and their votes will have no bearing on the ultimate outcome. The decision to

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limit voters' options thus helps C, in this case, as it deprives L of a certain number ofvotes that exhaust (due to the restriction) before they reach himlher.

Ifthe Director favors L, then his political goal (electing L) is best served by imposing nolimit on voters' options. This will minimize the number of ballots cast by minorcandidates that exhaust before they transfer to one of the major candidates. It willaccordingly benefit L, as he is the likely net beneficiary of such transfers..Note that the example just given is a simply a stylized version of recent mayoral electionsin San Francisco. The conditions that need to be met-two main candidates, one moreand one less conservative; a smattering ofminor candidates, mostly on the left-arealready met. Moreover, the Director of Elections will have a good idea about how manycandidates there are likely to be, when he must decide whether to restrict voters'rankings; and it is likely that he will be well informed about the political leanings of eachcandidate. Even with little effort, therefore, he will be in a position to estimate which ofthe major candidates will be the net beneficiary of late transfers. With someinvestigation-say a proprietary poll of the San Francisco electorate-the size of theadvantage or disadvantage could be calculated more finely.

To clarify how a candidate with leverage over the Director of Elections might proceed, ifunethical, imagine the following. A candidate for mayor commissions a poll of the S.F.electorate shortly before the Director of Elections must decide whether to restrict voters'options or not. The poll asks each respondent to rank as many of the candidates formayor as slhe wishes, just as s/he would be asked at election time if no restrictions wereimposed. Using the poll responses, one can calculate the early- and late-transfer vote foreach of the two main candidates. The early-transfer vote for a candidate is simply thesum of all votes that accrue to that candidate by the third round of counting; the late­transfer vote for a candidate is the sum of all votes that accrue to that candidate after thethird round of counting. Suppose that T percent of late-transfer votes go to the unethicalcandidate, while 100-T percent go to his or her main rival. Since this is the result of alimited sample of S.F. voters, there will be some uncertainty regarding whether, in thefull electorate, the same percentage breakdown would occur. Using standard statisticaltests, however, one equId classify the poll results as follows: T is significantly below50%; T is significantly above 50%; or neither. In the first case, allowing the late-transfervotes will likely harm the unethical candidate's chances of winning and s/he shouldtherefore suppress them by instructing the Director of Elections to restrict voters' options.In the second case, allowing the late-transfer votes will likely aid the unethicalcandidate's chances of winning and s/he should therefore facilitate them by instructingthe Director of Elections not to restrict voters' options. In the third case, the late-transfervotes will neither clearly harm nor clearly aid the unethical candidate, and so s/he wouldbe indifferent regarding whether the Director of Elections restricted voting options or not.

It is an easy matter to estimate what proportion of late-transfer votes a given candidatewill get, based on proprietary polling information. It is also an easy matter for candidatesto see that, if they are likely to get less than 50% of the late-transfer vote, then theyshould want to suppress it, while if they are likely to get more than 50%, they should

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want to facilitate late transfers. The only IRV or IRV-like system of which I am aware,past or present, that actually allows candidates potentially to do something about theirpreferences for allowing or disallowing late-transfer votes is San Francisco's.

Whether S.F. politicians exploit their opportunity or not remains to be seen but it can benoted that politicians in other systems using IRV have long recognized the importance ofdeciding how many rankings voters can or must express. In Australia, which has usedIRV to elect members of its House ofRepresentatives since 1919, it is the right-wingparties that have historically been split (into the National and Liberal parties). Therightist parties have consistently supported Australia's requirement that voters rank allcandidates on the ballot. The reason for their support is that mandatory ranking of allcandidates ensures, in districts where both a National and a Liberal candidate run, that allvotes will transfer. Both parties issue how-to-vote cards to their supporters, instructingthem to vote National first, then Liberal (or vice versa). In this way, neither party pays acost from running separate candidates. Recognizing the value of mandatory ranking to itsopponents, the Labour party in Australia has often (although not always) opposed theprovision or argued for a return to plurality voting. Had the party in government inAustralia been given the right to decide whether rankings were mandatory or not, thenone would probably have seen a strong pattern (Labour removing the requirement,National/Liberal imposing it). Similarly, in San Francisco, one might find Directors ofElections who favor the more conservative leading candidate imposing a limit on howmany rankings voters can list on the ballot, while Directors favoring the more liberalleading candidate impose no such limits.

A morning-after scenario in San FranciscoConsider the following morning-after scenario for the next San Francisco mayoralelection, ifit is held under the proposed restricted-IRV system. At the final vote count,the ballots will be sorted into five mutually exclusive categories. There will be Fl ballotsthat, in the final count, provide votes for the winning candidate; F2 ballots that, in thefinal count, provide votes for the runner-up; Xl ballots that extinguished and ranked onlyone candidate; X2 ballots that extinguished and ranked exactly two candidates; and X3ballots that extinguished and ranked exactly three candidates. All valid ballots will fallinto one of these five.,categories.

Suppose that Fl < F2 + X3. It will then be possible for the losing candidate and hislhersupporters to argue that, had voters not been restricted to three rankings, the outcome ofthe election would have been different. IfF1 and F2 are nearly equal, and X3substantially greater than the margin of victory, F1 - F2, then the argument would beplausible. Unfortunately for public confidence in the electoral process, there would be noway to prove or disprove the claims made on behalf of the losing candidate. Thelegitimacy of the victor's claim to office would thus be permanently in doubt.

Ballot formatAnother unusual feature of the proposed San Francisco IRV process is the ballot format.Most IRV systems employ a very simple ballot. The Australians, for example, list eachcandidate's name once with a box next to it, and the voter is instructed to write the

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number 1 in the box next to his first choice, the number 2 in the box next to his secondchoice, and so on (see Exhibit 1). The Irish, too, use this format in their by-elections (seeExhibit 2). Another format (Exhibit 3) lists the names once and invites the voter toindicate whether they wish to vote for this candidate "as their first choice," "as theirsecond choice," and so on. San Francisco, in contrast, proposes to print all candidates'names three times. The voter, if they read and understand the information at the top ofeach block ofnames, then votes three times: the first time for their first choice, thesecond time for their second choice, and the third time for their third choice. The S.F.ballot thus has far more words, and more confusing words, than does the Australian orIrish ballots-where the IRV system has been used the longest.

San Francisco's ballot format will presumably increase the ballot spoilage rate and themayoral "roll-off' rate for all voters. I I Previous research, however, shows that theimpact of confusing ballot formats is greater on the less educated, minority and non­English-speaking segments of the population. Kousser, for example, explains how theintroduction of a complex eight-ballot procedure in South Carolina in 1882 was intended,and had the effect of, disfranchising illiterates (with the primary target being formerslaves).12 More recently, Darcy and Schneider show how more confusing ballotswidened the gap in participation between blacks and whites in Oklahoma in the mid­1980s.13 Given these previous findings-and common sense-one would expect SanFrancisco's peculiar ballot format for the 2003 IRV election to have the effect of dilutingminority groups' influence on the outcome.

The reason that San Francisco chose such an unusual ballot format is presumably that theelection administrators feared that a hand-count of ballots in which voters could rank asmany candidates as they wished would be technically overwhelming. There are twopoints to make in this regard.

First, the Papua New Guineans successfully administered a hand-counted systemnationwide from 1964-72, while allowing voters to express full preferences. Similarly,the Irish have successfully administered hand counting of by-election results since the1920s, again allowing voters to express full preferences. In both nations, there weresometimes fields of c,andidates as large as that expected in the San Francisco mayoralrace. For example, in the Dublin North by-election of 23 October 1998, there were 18candidates and it took 14 counts before the election was decided. Thus, it is technicallyfeasible to hand count IRV elections, even when voters are allowed to express as manyrankings as they wish.

11. When a voter shows up at the polls, votes for some offices or propositions on the ballot, but does notvote in the mayoral race, they are said to "roll off' the ballot for that particular race. Put another way, onecalculates the number of all voters who do cast valid votes in the mayoral race, and divides this by thenumber of all voters who cast valid ballots (with a valid vote for at least one item on the ballot). Theinverse of this percentage is the roll off rate for the mayoral election.12. Kousser, J. Morgan. 1974. The Shaping ofSouthern Politics: Suffrage Restriction and theEstablishment ofthe One-Party South, 1880-1910. New Haven: Yale University Press, p. 50.13. Darcy, R., and Anne Schneider. 1989. "Confusing Ballots, Roll-of, and the Black Vote." WesternPolitical Quarterly 42(3):347-64.

13

Second, the fear of a technically difficult task will be realized only in the circumstancesin which restricting voters' rankings is most likely to affect the outcome. Suppose thatvoters are allowed to rank as many candidates as they wish but so few rank more thanthree that the outcome is the same as it would have been had they been restricted to threerankings. In this case, the administrative difficulty of counting the ballots is not in factmuch greater with full ranking than it would be with restricted ranking. If, on the otherhand, the administrative difficulty of counting the ballots is greater with full than withrestricted ranking, this can only be because many voters would choose to rank more thanthree, in which case restricting them is likely to affect the outcome. Thus, the countingcosts can be avoided only at the likely expense of affecting the outcome.

BARTON, NSW

Appendix 1

84,332 enrolled, 80,023 (94.9%) voted

14

====================================================================Suburban Sydney: Brighton, Hurstville, Kogarah, Rockdale

1998 two-party majority: ALP over Liberal 09.8Effect of redistribution: no change

Janette Brennan Lib 28,198 37.7 (+02.8)John Lau Unity 1,375 01. 8 (-02.4)David Rystrand ON 2,725 03.6 (-03.2)Chris Harris Grn 2,168 02.9 (+01. 3)David Barker CTA 1,081 01.4Robert McClelland * ALP 35,871 48.0 (-01.7)Michelle Adair AD 3,328 04.4 (+01. 7)

5,277 (06.6%) informal 74,746

2nd count: Barker's 1,081 votes distributed

Brennan 432 (40.0) 28,630 38.3Lau 56 (05.2) 1,431 01. 9Rystrand 168 (15.5) 2,893 03.9Harris 115 (10.6) 2,283 03.0McClelland * 198 (18.3) 36,069 48.3Adair 112 (10.4) 3,440 04.6

> 1,081 74,746

3rd count: Laurs 1,431 votes distributed

Brennan 358 (25.0) 28,988 38.8Rystrand 68 (04.7) 2,961 04.0Harris 198 (13.8) 2,481 03.3McClelland * 580 (40.5) 36,649 49.0Adair 227 (15.9) 3,667 04.9

> 1,431 74,746

4th count: Harris's 2,481 votes distributed

BrennanRystrandMcCLELLAND *Adair

>

327 (13.2)218 (08.8)893 (36.0)

1,043 (42.0)

2,481

29,3153,179

37,5424,710

74,746

39.204.250.206.3

5th count: Rystrand's 3,179 Yotes distributed

15

BrennanMcCLELLAND *Adair

>

1,997 (62.8)768 (24.2)414 (13.0)

3,179

31,31238,3105,124

74,746

41. 951.206.9

6th count: Adair's 5,124 Yotes distributed

BrennanMcCLELLAND *

>

1,561 (30.5)3,563 (69.5)

5,124

32,87341,873

74,746

44.056.0

06.0 03.8 to Lib

Robert Bruce McClelland (born 1958): Elected 1996, 1998, 2001

ADELAIDE, SA

Appendix 2

86,141 enrolled, 81,669 (94.8%) voted

16

====================================================================Inner Adelaide: Hindmarsh, Kilburn, Prospect, Walkerville

1998 two-party majority: Liberal over ALP 00.9Effect of redistribution: 00.3 shift to LiberalNew notional majority: Liberal over ALP 01.2

Lynne Osborn Grn 4,638 06.0 (+02.8)Tim Stanley ALP 28,732 37.1 (-00.1)Hon Trish Worth * Lib 34,258 44.2 (+00.8)Lee Peacock ON 1,630 02.1 (-03.3)Sue Mann AD 8,255 10.6 (+00.9)

4,156 (05.1%) informal 77,513

2nd count: Peacock's 1,630 votes distributed

OsbornStanleyWorth *Mann

>

337 (20.7)457 (28.0)598 (36.7)238 (14.6)

1,630

4,97529,18934,856

8,493

77,513

06.437.745.011.0

3rd count: Osborn's 4,975 votes distributed

StanleyWorth *Mann

>

1,635 (32.9)519 (10.4)

2,821 (56.7)

4,975

30,82435,37511,314

77,513

39.845.614.6

4th count: Mann'~,11,314 votes distributed

StanleyWorth *

>

7,761 (68.6)3,553 (31.4)

11,314

38,58538,928

77,513

49.850.2

00.2 01.0 to ALP

Patricia Mary Worth (born 1946): Elected 1993, 1996, 1998, 2001Parliamentary Secretary to the Minister for Education, Training andYouth Affairs to 26 November 2001Parliamentary Secretary to the Minister for Health and Ageing from26 November 2001

17

Appendix 3

In this appendix, it is shown first that El-the number of final-count votes for theultimate winner that come from ballots ranking the ultimate winner in one ofthe topthree spots-must be at least as great as the ultimate winner's vote at the third count.Note that this is not just saying that the ultimate winner gets at least as many votes at thefinal count as s/he does at the third count-which is true but tautological. Rather, thepoint is that the ultimate winner's final-count votes/rom a certain subset a/ballots (thoseranking her or him in one of the top three spots) still exceed her third-count votes from allsources.

The quickest way to see that the claim must be true is to note that all the votes theultimate winner receives at the third count must come from ballots ranking her or him inone of the top three spots. Supposing one accepted this condition as true, the ultimateconclusion follows trivially, as one is now simply saying that the ultimate winner gets atleast as many votes from a fixed subset of ballots at the final as at the third count. So,why must it be true that all the votes the ultimate winner receives at the third count comefrom ballots ranking her or him in one of the top three spots?

We know that the ultimate winner's vote at the third count can be expressed as Tl (3) =t1 (I) + t1 (2) + t1 (3), where t1 (1) is the number of new votes that candidate 1 receives at thefirst count (i.e., all his/her first-preference votes), t1 (2) is the number of new votes thatcandidate 1 receives at the second count (i.e., all his/her transfer votes from the first­eliminated candidate), and t1 (3) is the number of new votes that candidate 1 receives at thethird count (i.e., all his/her transfer votes from the second-eliminated candidate). All ofthe votes that the candidate receives at the first count must rank him or her first (if theyranked someone else first, then the vote would go to that other person). All of thetransfer votes that the candidate receives from the first-eliminated candidate must rankhim or her second (if they ranked someone else second, then the vote would go to thatother person). Finally, all of the transfer votes that the candidate receives from thesecond-eliminated candidate can be divided into those that rank the first-eliminatedcandidate second and those that do not. Among the first category ofballots, the ultimatewinner gets the transfer vote (at the third round) only if s/he is ranked third. Among thesecond category ofhallots, the ultimate winner gets the transfer vote (at the third round)only if s/he is ranked second. All told, then, any vote received in any of the first threerounds must come from a ballot ranking the recipient in one of the top three spots. Thus,El ~ t1 (1) + tl (2) + t1 (3).

Any vote that candidate 1 receives at the fourth count, or any later count, could be from aballot ranking him/her fourth or lower. This is because there are two eliminatedcandidates by the fourth count, three eliminated candidates at the fifth count, and so on.Thus, a new vote received by candidate 1 at the fourth (fifth, sixth, ... ) count could comefrom a ballot that ranks the candidate eliminated at the round in question first, the first­eliminated candidate second, and the second-eliminated candidate third. Absent ballot­image data, one cannot logically rule out this possibility. Thus, it is possible that El =t1 (I) + t1 (2) + t1 (3).

18

A similar argument suffices to show that E2 must be at least as great as the ultimaterunner-up's vote at the third count. Thus, it is possible that El < E2, whenever theultimate winner's third-count vote total is less than the ultimate runner-up's final votetotal. This follows because, as shown above, El could be as low as t1 (1) + t1 (2) + t1 (3); andE2 could be as large as the runner-up's final-count vote, Tit). (There are unusualsituations in which one can deduce that E2 must be smaller than Tit). However, theseconditions do not arise in any of the cases identified empirically in the Australian data asbeing ones in which the ranking restriction might affect the outcome.)

J J'..:'-",:'1 t,\r:,,- "-,;;' {~:ltl ;rl\,....,:.'_1'1

Exhibit 1 19From David Farrell, Electoral Systems: A ComparativeIntroduction, London/New York: Palgrave 2001

BAU..OT PAPERHOUSEOF REPRESENTATIVES

WESTERN AUSlRAUAELE&1GRAL DIVISIONOf'

MOORE

Numbertileboxes from rto 5

in the orderofrourchoice.

D LLOYD. Alan AAUSTRALIAN DEMOCRATS

O WATSON, MarkGREY POWER

O FILING. PaulLIBERAL

O STEELS, BrianTHE GREENS (W.A.)

.D BLANCHARD, AllenAUSJRAlJAN LABOR PARTY (ALP)

Reqtembs•.numbere!!IY boxto make yourvole count.

~C

Figure 3.2 An Australian alternative vote ballot paper

Exhibit 2 20

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Exhi bit 3 21

OFFICIAL GENERAL ELECTION BALLOT,INSTRUCTIONS TO VOTER

A. To vote, complete the arrow(s* ..... pointing to your first choice(s), like this• •B. You may also indicate your alternate choice candidates, in case you first choice is eliminated in a runoff, by by connecting thearrow in line with the 2nd choice, 3rd choice, or other ranking in the section of the ballot marked off for those alternate candidates.Marking asecond, third, or subsequent choice cannot help defeat your first choice candidate.C.To vote for aperson whose name is not printed on the ballot, write the candidate's name on the line provided AND complete the arrow.D. If you wrongly mark, tear or deface the ballot, return it to an election offical and obtain another.

For US Senator For Representative to CongressVote for not more than ONE first choice Vote for not more than ONE first choice

HUGH DOUGLAS, Arlington as 1st choice • • MARK W. ABAIR, Calais as 1st choice • •Libertarianas 2nd choice. • Democratic

as 2nd choice. •as 3rd choice • • as 3rd choice. •as 4th choice • • as 4th choice • •as 5th choice • • as 5th choice • •

PATRICK LEAHY, Burlington as 1st choice • • NATALIE G. ROBERTS, as 1st choice • •Democraticas 2nd choice. • Richford Green

as 2nd choice. •as 3rd choice • • as 3rd choice • •as 4th choice • • as 4th choice • •as 5th choice • • as 5th choice • •

FRED H. TUTTLE, Tunbridge as 1st choice • • CALEB THOMAS, Barton as 1st choice • •Republicanas 2nd choice. • Republican

as 2nd choice. •as 3rd choice • • as 3rd choice. •as 4th choice • • as 4th choice • •as 5th choice • • as 5th choice • •

BART VANCOVINGTON, as 1st choice • • KATHRYN WILSON, Putney as 1st choice • •Brattleboro Independent as 2nd choice. • Independent as 2nd choice. •

as 3rd choice • • as 3rd choice • •as 4th choice • • as 4th choice • •as 5th choice • • as 5th choice • •as 1st choice • • as 1st choice • •

write in as 2nd choice. • write in as 2nd choice. •as 3rd choice • • as 3rd choice • •as 4th choice • • as 4th choice. •as 5th choice • • as 5th choice • •

GaryW. COX2003

22

Department ofPolitical Science 8931 Nottingham PlaceUniversity of California, San Diego La Jolla, California 92037-2133La Jolla, California 92093-0521

(858) 534-1428 (office) Born: September 23, 1955(858) 534-7130 (fax) Patuxent River, [email protected] Spouse: deceased.http://weber.ucsd.edul~gcox Child: Dylan Gregory Cox

CURRICULUM VITAE

EducationB.S. California Institute ofTechnology, 1978 (History - with honors).Ph.D. California Institute of Technology, 1982 (Social Science).

DissertationTitle: Party and Constituency in Victorian BritainDate of Completion: September 1982Primary Advisors: Bruce E. Cain and J. Morgan Kousser

Honors and awardsSamuel H. Beer Dissertation Prize, 1983.Richard F. Fenno Prize (from Section on Legislative Studies, APSA), 1993.Fellow of the John Simon Guggenheim Memorial Foundation, 1995-96.Fellow of the American Academy of Arts and Sciences (elected in 1996).The CQ Press Award (from Section on Legislative Studies, APSA), 1997.Woodrow Wilson Foundation Award (APSA), 1998.Best Book Award (from Section on Political Economy, APSA), 1998.Gregory M. Luebbert Prize (from Section on Comparative Politics, APSA), 1998.

Employment1982-84 Assistant Professor, Department of Government, University ofTexas at

Austin1984-85 Visiting Assistant Professor, Dept ofPolitical Science, Washington

University in St. Louis1985-86 Visiting Associate Professor of Political Economy, School ofBusiness,

Washington University in St. Louis1986-87 Associate Professor, Department of Government, University of Texas at

Austin

23

1987-90 Associate Professor, Dept ofPolitical Science, University of California, SanDiego

1990- Professor, Department ofPolitical Science, University of California, SanDiego

Research grantsUniversity ofTexas University Research Institute Grants, 1982, 1983.

National Science Foundation, Political Science Program (SES-8306032, $17,955,"Electoral Behavior in Double-Member Districts") 1983-4.

National Science Foundation, Political Science Program (SES-8811022, $201,602,"Formal Models of Committee Behavior"), 1988-90, with Mathew D. McCubbins.

National Science Foundation, Political Science Program (SES-9022882, $69,993,"Formal Models of Parties and Committees"), 1990-92, with Mathew D. McCubbins.Plus an REU supplement of$5,000.

University of California, San Diego, COR Grants: 1988, 1990, 1995, 1996, 1999.

National Science Foundation, Political Science Program (SES-9208753, $60,000,"Refining Duverger's Law Using District Level Theory and Data"), 1992-93, withMatthew Soberg Shugart.

National Science Foundation, Political Science Program (SBR-9422874, $20,000,"Lijphart Elections Archive"), 1995-6, with Matthew Soberg Shugart.

National Science Foundation, Political Science Program (SBER-9631784, $8,000), 1996­97. David Samuels' dissertation training grant.

National Science Foundation, Political Science Program (SBR-9730547, $77,678,"Strategic Redistricting and its Political Consequences"), 1998-99.

National Science Foundation, Political Science Program (SES-9905224, $175,855,"Agenda Power in Democratic Legislatures"), 1999-2001, with Mathew D.McCubbins.

Articles1981. "Turnout and Rural Corruption: New York as a Test Case." American Journal of

Political Science 25:646-63. [Co-author: J. Morgan Kousser]

1982. "Log-Linear Analysis of Contingency Tables: An Introduction for HistoriansWith an Application to Thernstrom on the 'Floating Proletariat.'" Historical Methods15(Fall):152-169. [Co-authors: J. Morgan Kousser and David W. Galenson]

1984. "A Ham Sandwich Theorem for General Measures." Social Choice and WelfareI(May):75-83. [Co-author: Richard D. McKelvey]

24

1984. "The Development ofParty Voting in England, 1832-1918." Historical SocialResearch 41(Ju1y):2-37. [8306032]

1984. "An Expected Utility Model of Electoral Competition." Quality and Quantity18(August):337-349.

1984. "Non-Collegial Simple Games and the Nowhere Denseness of the Set ofPreference Profiles Having a Core." Social Choice and Welfare 1(September):159­164.

1984. "Strategic Electoral Choice in Multi-Member Districts: Approval Voting inPractice?" American Journal ofPolitical Science 28(November):722-738.[8306032]

1984. "Policy Choice as an Electoral Investment." Social Choice and Welfare 1:231-242.[Co-authors: Mathew D. McCubbins and Terry Sullivan]

1984. "Electoral Equilibrium in Double-Member Districts." Public Choice 44:443-451.

1985. "Electoral Equilibrium Under Approval Voting." American Journal ofPoliticalScience 29(February):112-118.

1986. "The Development ofa Party-Oriented Electorate in England, 1832-1918." BritishJournal ofPolitical Science 16(April):187-216. [8306032]

1986. "Electoral Politics as a Redistributive Game." Journal ofPolitics 48(May):370­389. [Co-author: Mathew D. McCubbins]

1987. "Electoral Equilibria Under Alternative Voting Institutions." American Journal ofPolitical Science 31 (February):82-108.

1987. "The Core and the Uncovered Set." American Journal ofPolitical Science31(May):408-422.

1989. "Undominated Candidate Strategies Under Alternative Voting Rules."Mathematical Modelling 12:451-60.

1990. "Centripetal and Centrifugal Incentives in Electoral Systems." American JournalofPolitical Science 34:903-935. [8811022]

1991. "SNTV and d'Hondt are 'Equivalent'." Electoral Studies 10:118-32. [8811022]

1991. "On the Decline ofParty Voting in Congress." Legislative Studies Quarterly16:547-70. [8811022]

25

1992. "Suffrage Expansion and Legislative Behavior in Nineteenth Century Britain."Social Science History 16:539-60. [Co-author: James Ingram] [8811022]

1993. "The Electoral Fortunes of Legislative Factions in Japan." American PoliticalScience Review 87:577-89. [Co-author: Frances Rosenbluth] [9022882]

1993. "The Development of Collective Responsibility in the u.K." ParliamentaryHistory 13: 32-47. Reprinted in Computing Parliamentary History: George III toVictoria, ed. John A. Phillips. Edinburgh: Edinburgh University Press, 1994.

1993. "The Increasing Advantage of Incumbency in the American States." LegislativeStudies Quarterly 18:495-514. [Co-author: Scott Morgenstern] [9208753]

1994. "A Note on Crime and Punishment." Public Choice 78:115-124. [9022882]

1994. "Reducing Nomination Errors: Factional Competition and Party Strategy inJapan." Electoral Studies 13:4-16. [Co-author: Frances Rosenbluth] [9208753]

1994. "Bonding, Structure and the Stability of Political Parties: Party Government in theHouse." Legislative Studies Quarterly 19(May):215-231. [Co-author: Mathew D.McCubbins] [9022882]Reprinted in Shepsle, Kenneth and Weingast, eds., Positive Theories ofCongressional Institutions. Ann Arbor: University of Michigan Press, 1995.

1994. "Strategic Voting Equilibria Under the Single Non-Transferable Vote." AmericanPolitical Science Review 88:608-621. [9208753]

1995. "The Incumbency Advantage in Multi-Member Districts: Evidence from the U.S.States," with Scott Morgenstern, Legislative Studies Quarterly 20:329-350.[9208753]

1995. "Anatomy of a Split: The Liberal Democrats of Japan." Electoral Studies 14:355­76. [Co-author: Frances Rosenbluth] [9208753]

1995. "In the Absence of Vote Pooling: Nomination and Vote Allocation Errors inColombia." Electoral Studies 14:441-460. [Co-author: Matthew S. Shugart][9208753]

1996. "Why Did the Incumbency Advantage in U.S. House Elections Grow?" AmericanJournal ofPolitical Science 40:478-97. [Co-author: Jonathan Katz]

1996. "Is the Single Non-Tran~ferableVote Superproportional? Evidence from Japanand Taiwan." American Journal ofPolitical Science 40:740-755.

1996. "Strategic Voting Under Proportional Representation." Journal ofLaw, Economicsand Organization 12(October):299-324. [Co-author: Matthew S. Shugart]

26

1997. "Electoral Institutions, Cleavage Structures and the Number of Parties." AmericanJournal ofPolitical Science 41 :149-174. [Co-author: Octavio Amorim Neto]

1997. "Toward a Theory of Legislative Rules Changes: Assessing Schickler and Rich'sEvidence." American Journal ofPolitical Science 41: 1340-1375. [Co-author:Mathew D. McCubbins]

1998. "The Cost of Intraparty Competition: The Single, Nontransferable Vote andMoney Politics in Japan." Comparative Political Studies 31:267-91. [Co-author:Michael F. Thies]

1998. "Mobilization, Social Networks and Turnout: Evidence From Japan." WorldPolitics 50:447-474. [Co-authors: Frances Rosenbluth and Michael F. Thies]

1999. "The Empirical Content of Rational Choice Theory: A Reply to Green andShapiro." Journal ofTheoretical Politics 11(April):147-169.

1999. "Electoral Reform and the Fate ofFactions: The Case ofJapan's LiberalDemocratic Party." British Journal ofPolitical Science 29(1):33-56. [Co-authors:Frances M. Rosenbluth and Michael F. Thies]

1999. "How Much is Majority Status in the U.S. Congress Worth?" American PoliticalScience Review 93(June):299-310. [Co-author: Eric Magar]

1999. "The Reapportionment Revolution and Bias in U.S. Congressional Elections."American Journal ofPolitical Science 43(July):812-41. [Co-author: Jonathan N.Katz] [9730547]

1999. "Electoral Rules and Electoral Coordination." Annual Review ofPolitical Science2:145-161.

1999. "Electoral Rules and the Calculus of Mobilization." Legislative Studies Quarterly24:387-420. .

2000. "Electoral Rules, Career Ambitions, and Party Structure: Conservative Factions inJapan's Upper and Lower Houses." American Journal ofPolitical Science 44:115­122. [Co-authors: Frances Rosenbluth and Michael F. Thies]

2000. "How Much Does Money Matter? 'Buying' Votes in Japan, 1967-1990."Comparative Political Studies 33:37-57. [Co-author: Michael F. Thies]

2000. "On the Effects of Legislative Rules." Legislative Studies Quarterly 25:169-192.

27

2000. "Agenda Power in the Japanese House of Representatives." Japanese Journal ofPolitical Science 1:1-22. [Co-authors: Mikitaka Masuyama and Mathew D.McCubbins]

2001. "Latin America's Reactive Assemblies and Proactive Presidents." ComparativePolitics 33(2):171-190. [Co-author: Scott Morgenstern] [Also appeared as 2001."Legislaturas reactivas y presidentes proactivos en America Latina." DesarolloEconomic041 (163):373-94.] [Also appeared as 2002. "Epilogue: Latin America'sReactive Assemblies and Proactive Presidents." In Scott Morgenstern and BenitoNacif, eds. Legislative Politics in Latin America. Cambridge: CambridgeUniversity Press, pp. 446-68.]

2001. "Agenda Setting in the U.S. House: A Majority-Party Monopoly?" LegislativeStudies Quarterly 26(2): 185-210.

2002. "On Measuring Partisanship in Roll Call Voting: The U.S. House ofRepresentatives, 1877-1999." American Journal ofPolitical Science 46(3):477­89. [Co-author: Keith Poole.]

Notes1984. "Universalism and Allocative Decision-Making in the Los Angeles County Board

of Supervisors." Journal ofPolitics, 46(May):546-555. [Co-author: Tim Tutt]

1988. "Closeness and Turnout: A Methodological Note." Journal ofPolitics50(August):768-775.

1989. "Closeness, Expenditure, Turnout: The 1982 U.S. House Elections." AmericanPolitical Science Review 83 (March):217-32. [Co-author: Michael C. Munger]

1991. "Comment on Gallagher's 'Proportionality, Disproportionality and ElectoralSystems'.", Electoral Studies 10:348-52. [Co-author: Matthew Soberg Shugart][9022882]

1992. "The Origin of Whip Votes in the House of Commons." Parliamentary History 11,pt. 2:278-85. [8811022]

1994. "Seat Bonuses Under the Single Non-Transferable Vote System: Evidence fromJapan and Taiwan." Comparative Politics 26:221-236. [Co-author: Emerson Niou][9208753] Reprinted in Bernard Grofinan, Sung-Chull Lee, Edwin Winckler, andBrian Woodal, eds., Elections in Japan, Korea, and Taiwan Under the Single Non­Transferable Vote: The Comparative Study ofAn Embedded Institution (Ann Arbor:University ofMichigan Press, 1999.)

28

1996. "Factional Competition for the Party Endorsement: The Case of Japan's LiberalDemocratic Party." British Journal ofPolitical Science 26:259-297. [Co-author:Frances Rosenbluth]

1997. "The Identification of Government Whips in the House of Commons, 1830-1905."Parliamentary History 16:339-58. [First author = Sir John Sainty]

1999. "A Comment on Browne and Patterson's 'An Empirical Theory of RationalNominating Behaviour Applied to Japanese District Elections'." British Journal ofPolitical Science 29:565-575.

2001. "Comment on "Japan's Multimember SNTV System and Strategic Voting: The'M+l' Rule and Beyond." Japanese Journal ofPolitical Science 2(2):237-40.

2001. "Introduction to special issue on estimating legislators' preferences with roll calldata." Political Analysis 9(3):189-91.

Chapters in edited volumes1990. "Multicandidate Spatial Competition," in James Enelow and Melvin Hinich, eds.,

Advances in the Spatial Theory ofVoting. (New York: Cambridge University Press).[8811022]

1991. "Fiscal Policy and Divided Government,", in Gary W. Cox and Samuel Kernell,eds., The Politics ofDivided Government (Boulder: Westview Press). [Co-author:Mathew D. McCubbins]

1994. "Party Coherence on Roll Call Votes in the U.S. House ofRepresentatives," inJoel Silbey, ed., Encyclopedia ofthe American Legislative System, Vol. II (NewYork: Charles Scribner's Sons, 1994). [Co-author: Mathew D. McCubbins]

1995. "The Structural Determinants of Electoral Coherence,", in Peter Cowhey andMathew McCubbins, eds., Structure and Policy in Japan and the United States (NewYork: Cambridge University Press), pp. 19-34. [Co-author: Frances Rosenbluth][9208753]

1999. "Measuring the Ties That Bind: Electoral Cohesiveness in Four Democracies," inBernard Grofman, Sung-Chull Lee, Edwin Winckler, and Brian Woodall, eds.,Elections in Japan, Korea, and Taiwan Under the Single Non-Transferable Vote:The Comparative Study ofAn Embedded Institution (Ann Arbor: University ofMichigan Press). [Co-authors: Kathy Bawn and Frances Rosenbluth]

2001. "The institutional determinants of economic policy outcomes." In Mathew D.McCubbins and Stephan Haggard, eds., Presidents, Parliaments and Policy (NewYork: Cambridge University Press), pp. 21-63. [Co-author: Mathew D.McCubbins]

29

2002. "Agenda power in the House of Representatives." In David W. Brady andMathew D. McCubbins, eds., Party, Process, and Political Change in Congress:New Perspectives on the History ofCongress. Pages 107-45. Palo Alto:Stanford University Press. [Co-author: Mathew D. McCubbins]

2002. "Agenda power in the Senate, 1877 to 1986." In David W. Brady and Mathew D.McCubbins, eds., Party, Process, and Political Change in Congress: NewPerspectives on the History ofCongress. Pages 146-65. Palo Alto: StanfordUniversity Press. [Co-authors: Andrea Campbell and Mathew D. McCubbins]

Forthcoming. "On the systemic consequences of redistricting in the 1960s." In PeterGalderisi, ed. Redistricting in the New Millennium. Lexington Books.

BooksThe Efficient Secret: The Cabinet and the Development ofPolitical Parties in Victorian

England (Cambridge: Cambridge University Press, 1987). [8306032]

Legislative Leviathan: Party Government in the House (Berkeley: University ofCalifornia Press, 1993). [Co-author: Mathew D. McCubbins] [8811022; 9022882]

Making Votes Count: Strategic Coordination in the World's Electoral Systems(Cambridge: Cambridge University Press, 1997). [9208753; 9422874]

Elbridge Gerry's Salamander: The Electoral Consequences ofthe ReapportionmentRevolution (Cambridge: Cambridge University Press, 2002). [Co-author: JonathanN. Katz] [9730547]

Edited BooksThe Politics ofDivided Government (Boulder: Westview Press, 1991). [Co-editor:

Samuel Kernell]

Other Publications1985. "On the UseofParty Labels in Victorian England." British Politics Group

Newsletter I (Spring):5-6.

1988. "Recent Developments in Statistical Inference: Quasi-Experiments andPerquimans County." Historical Methods 21 (Summer): 140-42.

1988. "Appendix 1: Analysis ofVoting in Multi-Member Seats, 1874-1880." In F.W.S.Craig, ed., British Parliamentary Election Results, 1832-1885 (Dartmouth:Parliamentary Research Services). [Co-compiler: F.W.S. Craig]

1995. "A Comment on 'The Great Reform Act of 1832 and the Political Modernizationof England' ." Letter to the Editor. American Historical Review 1OO(October): 1371­1373.

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1999. "Instability?" Boston Review XXIII, Number 1, pp. 16-7. Reprinted as"Instability?" In Robert Richie and Steven Hill, eds., Reflecting All ofUs: The Casefor Proportional Representation. Boston: Beacon Press.

2000. Eight entries in the International Encyclopedia ofElections, ed. Richard Rose.Washington, D.C.: CQ Press.

Research interestsComparative Study of Legislative and Electoral PoliticsFormal Theories ofPoliticsNineteenth-Century American and British Political HistoryAmerican Politics

Professional activitiesReferee:

American Journal ofPolitical Science, American Political Science Review, Journal ofPolitics, National Science Foundation, and many others.

Editorial Board:American Journal ofPolitical Science, 1985-1991.American Political Science Review, 1992-1995.Electoral Studies, 1996-.Journal of Law, Economics and Organization, 1997-.Legislative Studies Quarterly, 1997-2000.Political Analysis, 1998-.Japanese Journal ofPolitical Science, 1999-.British Journal of Political Science, 2000-.Journal ofTheoretical Politics, 2002­Annual Review ofPolitics, 2002-

Prize Committees:Member, Samuel H. Beer Prize Committee for 1986.Chair, Richard F. Fenno Prize Committee, 1995.Chair, Gregory Luebbert Prize Committee, 1996-7.Chair, CQ Prize Committee, 1997-98.Chair, Best Book in Political Economy Committee, 1999-2000.Member, Richard F. Fenno Prize Committee, 2000.Member, Gregory Luebbert Prize Committee, 2002.

Conferences:Section Chair, Western Political Science Association, 1993.Section Chair, American Political Science Association, 1995.

Other:Member, Board of Overseers, National Election Studies, 1995-1999.

31

Consultant, Comparative Study of Electoral Systems Project, ICORE, 1995- .Member, Council of the American Political Science Association, 1997-1999.Member, Advisory Council of the F. Clifton White Resource Center, IFES, 1998-.Member, Political Science Advisory Panel, National Science Foundation, 2000-2002.

Papers deliveredConventionsAmerican Political Science Association, 1987, 1988, 1990, 1993, 1995, 1996, 1997,

1999,2000,2001,2002,2003.Conference on Theories ofDemocratic Institutions, Taipei, Taiwan, 1992.Conference on the role of legislatures in Latin America, Mexico City, Mexico, 1998.Midwest Political Science Association, 1984, 1990, 1997, 1998.National Election Studies Research Conference (on the study of congressional elections),1996.Operations Research Society of America, 1986..Public Choice Society 1983, 1984, 1989.Social Science History Association, 1983.

UniversitiesCalifornia Institute ofTechnology, 1984, 1985, 1988, 1992.University of California, Berkeley, 1999.University of California, Los Angeles, 1986, 1989, 1990, 1991, 1996, 1999,2000.University of Chicago, 1985, 1994.Duke University, 1992, 1993, 1996.Harvard University, 1989, 1998, 1999.University of Houston, 2001.University of Illinois, Champaign-Urbana, 1991.Juan March Institute, 2003.University of Minnesota, 1997.University of Michigan, 1998.Northwestern Unive~sity, 1995.University ofNotre Dame, 1998.Ohio State University, 2000.University of Pennsylvania, 1988.Princeton University, 1990, 1997,2003.University ofRochester, 1999.Stanford University, 1985, 1986, 1989, 1999,2001 (twice).Washington University in St. Louis, 1984,2001.Yale University, 1993, 1994,2002 (twice), 2003.