Should Voting be Anonymous in Legislatures? Economics and Politics Research Group Seminar Universidade de Braslia - Oct. 14, 2015. RogØrio Mazali Catholic U. of Braslia Dept. of Economics JosØ A. Rodrigues-Neto Australian National U. School of Economics 12/02/2015 Mazali & Rodrigues-Neto (AETW 2015). Should Voting be Anonymous? 12/02/2015 1 / 36
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Should Voting be Anonymous in Legislatures? · 2015. 10. 14. · Should Voting be Anonymous in Legislatures? Most of the voting in Legislatures (in most countries) is open. Anonymous
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Should Voting be Anonymous in Legislatures?Economics and Politics Research Group Seminar
Universidade de Brasília - Oct. 14, 2015.
Rogério MazaliCatholic U. of BrasíliaDept. of Economics
José A. Rodrigues-NetoAustralian National U.School of Economics
If it becomes public that j voted for Pb , then uRj (Pj ) = �R < 0Otherwise, uRj (Pj ) = 0R = cost of losing her reputation because she was observed voting forproject Pb
Bribes:
uBj (Pj ) = Bj , the bribe payment received by j (may be zero)
Events occur in the following order:1 The constitution maker chooses an (observable) voting rule2 Reservation value V of the lobbyist is randomly draw3 Lobbyist observes V and proposes a bribe schedule4 Each voter j 2 J observes the bribe schedule and votes5 The simple majority winner project is implemented, payo¤s are realized
Let us start analyzing the case in which the Lobbyist can observevoters�preferences.Lobbyist can make tailor-made o¤ers to each voter infn0 + 1, � � � , ng.O¤ers are such that each voter j 2 fn0 + 1, � � � , ng is indi¤erent,that is:
Bj = R + (�1+ j/h)βThe lobbyist�s total expenditure is:
The expenditure of the Lobbyist to make project Pb the winnerdepends on whether the vote is open or anonymous.
If voting is anonymous, all voters will come to the lobbyist, after Pb�sapproval, and claim that they voted for Pb . The Lobbyist will have topay all voters, but R = 0:
SNonAn = (2n� 1)B = (n� h)(2n� 1)βh
(1)
If voting is open, then the Lobbyist can see how each Legislatorvoted, and pay accordingly. Since only n voters vote for Pb , theLobbyist pay these n voters.
The expenditure of the Lobbyist to make project Pb the winnerdepends on whether the vote is open or anonymous.
If voting is anonymous, all voters will come to the lobbyist, after Pb�sapproval, and claim that they voted for Pb . The Lobbyist will have topay all voters, but R = 0:
SNonAn = (2n� 1)B = (n� h)(2n� 1)βh
(3)
If voting is open, then the Lobbyist can see how each Legislatorvoted, and pay accordingly. Since only n voters vote for Pb , theLobbyist pay these n voters.
Non-Observable Legislators�Preferences 3: All but OneVoters Bribed
The Lobbyist will prefer to bribe all members of Legislature to bribingno one at all if V � SNonx , for x 2 fAn,Opg.If V < SNonx , it does not mean that will let Legislators vote withoutin�uencing the outcome.
The Lobbyist can randomly pick a Legislator and this voter will notreceive a bribe, and pass Pb with a positive probability:
If the randomly picked voter is in the Pivotal set fn0 + 1, . . . , ng,project Pb will fail;If the randomly picked voter is in f1, . . . , n0g [ fn+ 1, . . . , 2n� 1g,project Pb will pass.
Non-Observable Legislators�Preferences 6: All but kVoters Bribed
If bribing all but one voters does not yield a positive expected surplusto the Lobbyist, he can randomly pick more voters to leabe out of theo¤er and approve Pb with a smaller probability.
In expected value, such a strategy might yield a higher payo¤ thanbribing all voters or not bribing anyone at all.
Project Pb is approved if none of the left-out voters is in the Pivotalset fn0 + 1, . . . , ng.
Because n > h, we have that (2n� k � 1)! > (n+ bhc � k)!. Itfollows that variable V An,�k is an increasing function of k. Thisviolates our original assumption.There is no PBE in which some voters are bribed and some arenot.
This paper tries to shed some light over the issue of Legislature votepublic disclosure.
We modeled a legislature with mandatory voting (no abstentions) inwhich a lobbyist tries to in�uence the outcome towards an ine¢ cientproject.
PBE:
If the project is highly valued by the lobbyist, he will bribe all votersneeded to pass his bill.If the project has low value to the lobbyist, he will let the e¢ cientproject pass.No intermediate outcomes.
If the project is highly valued by the lobbyist, he will bribe all votersneeded to pass his bill.If the project has low value to the lobbyist, he will let the e¢ cientproject pass.For intermediate project values, if voters�utilities are not observable,the lobbyist will randomly bribe a number of voters smaller thanneeded to pass the bill with certainty:
The number of voters bribed increase with project value;Project probability of approval is a step function increasing in projectvalue.
In a Cursed Eq., if voters�preferences are observable, then the openvote rule yields a more e¢ cient outcome.
In a Cursed Eq., if voters�preferences are not observable, resultsdepend on parameter values:
High reputation costs R tend to bene�t the open vote rule;High importance of the issue voted to the voters (β) tends to bene�tthe anonymous vote rule;High importance of the issue voted to the lobbyist (V ) tends to bene�topen vote.