Democracy, Borders, & Legitimacy

Democracy, Borders, & Legitimacy

This is an argument about the relationship between democratic inclusion and instrumental justifications

of democracy. I show that any account of democracy that relies on the outcomes of democracy processes

to demonstrate democracy's value must have a congruent account of inclusion. Not only that, but

because different accounts of democracy rely on different and incompatible accounts of inclusion, these

accounts of democracy are themselves incompatible.

This paper is unique in that is simultaneously a philosophical argument and a computer simulation.

Written in literate coffeescript, the code described in the paper can also be run by the coffeescript compiler

to demonstrate the argument being described by the paper. The reader may generate both the argument in

PDF, or the simulation and results in HTML with the command coffee paper.coffee.md .

Best viewed in HTML with interactive graphs, the following links outline paper, installation, and

dependency requirements. A PDF version is also available with static images.

― Introduction ―

There are many ways one might justify democracy. One common approach is to point to the desirable

outcomes that democratic procedures bring about. Democracy in this light leads to good policy.

Sometimes the desirability of these outcomes is judged according to some independent criteria.

According to these accounts, there is some external standard for measuring the quality of a decision.

Epistemic accounts of democracy like Condorcet's Jury Theorem or David Estund's Epistemic

Proceduralism are like this. Truth exists independently of our beliefs; democratic processes track the

truth; so this gives us reason to value democracy.

Other times, we might judge the quality of democratic outcomes against some agent relative criteria.

Rather than rely on something external, the desirability of a particular result is assessed against some

internal standard. It isn't the collective decisions of democracy that matter per se but how those

collective decisions correspond with individual choices. We see this in utilitarian justifications of

democracy where majority voting maximises the expected utility of voter preferences. But one needn't

be a utilitarian to employ such an approach - Jean-Jacques Rousseau, for example, argued that majority

rule realises the general will of the people and this gives us reasons value it.

And for others still, it is not the particular content of democratic decision making that matters so much

as the e!ects that democratic processes have on the participants. Democracy changes people. This is

what John Stuart Mill, had in mind when he argued that democracy transforms the moral character of

its participants. Democratic participation makes good citizens.

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Call these accounts of democracy instrumental.

The outcome of any democratic procedure is a function, in part, of who gets to participate in that

procedure. Enfranchising some people rather than others, drawing the political line on a map in one

location rather than another, will often result in di!erent outcomes than would have otherwise

occurred, even when the same procedures are used. Who is included in a particular democracy a!ects

the outcomes of that democracy.

Some democratic processes are deterministic. Given the same inputs for some democratic system, the

result will always be the same. People vote according to their belief or preference and the voting

procedures employed determines a winning outcome. This is true for both naive voting, where voters

believe they alone determine the outcome, as well as strategic voting, where voters support a choice other

than their sincere preference in an attempt to increase the likelihood of an acceptable outcome.

For both naive and strategic voting, the outcome of a democratic process is fully a function of who

participates in that process. On one extreme, when voters are fully polarised, including or excluding a

single voter will change the outcome of the democratic process. At the other extreme of complete

consensus, over 50% of voters would need to be replaced for the outcome to change.

Other democratic processes however, are indeterministic. This may be because voters themselves don't

actually know how they will vote until the moment they cast their ballot, or because the decision

mechanism itself is random, as in the case of sortition or selection by lottery. Yet even in these cases,

the outcome of a democratic processes remain a function of who is included in that process, because

changing participants changes the likelihood of particular outcomes.

Who votes a!ects what is decided.

So when democracy is justified by way of its outcomes, and those outcomes are determined by who is

included in the democratic process, the question of who should be included becomes a matter of

fundamental importance for those accounts of democracy.

Yet the question of who ought be included in a political association - of how the demos ought be

bounded - presents a challenge to democratic theory. If we attempt to answer the question of inclusion

democratically, an infinite regress results. To vote on who gets to participate in a democracy first requires

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the identification of some prior group to make this decision, and to identify that prior group

democratically requires the identification a prior prior group, ad infinitum.

In what has become known as the Boundary Problem of Democratic Theory, no account of inclusion can be

shown to be compatible with a broad range of justifications of democracy. Accounts of inclusion based

on the status quo make the democratic outcomes contingent upon the accidents of history; those based

on nationality lack a clear and objective criteria of what nationality is; cultural and linguistic salience as

a criteria for inclusion ignores the reality of multiculturalism and multilingual communities; and

accounts based on coercion and a!ected interests are incompatible with the current system of nation-

states.

The Boundary Problem is a "fundamental issue in democratic theory" with "no theoretical solution to

the puzzle, only pragmatic ones". It is a problem that presents "an important practical limit to the scope

of democracy as a method of making collective decisions" but one "almost totally neglected by all the

great political philosophers who write about democracy". While a vexing issue for all accounts of

democracy, the Boundary Problem is especially problematic for instrumental accounts that rely on the

content of specific outcomes.

The question I wish to explore in this paper then is when is the Boundary Problem a problem for instrumental

accounts of democracy? Addressing why the Boundary Problem is a problem, or how it might be solved is

not my aim. Rather, I wish to explore the relationship between accounts of inclusion and accounts of

democracy and advance three claims that impact any answer to the question of who the people ought

be:

1. That accounts of democracy must be compatible with accounts of inclusion.

2. That di!erent accounts of democracy require di!ering, sometimes incompatible accounts of

inclusion.

3. That di!erent accounts of democracy that have incompatible accounts of inclusion are

themselves incompatible.

The first claim advances the existing literature on the Boundary Problem by making the link between

inclusion and justifications of democracy explicit. Often, political theorists approach the problem of

inclusion from a cosmopolitan position, arguing that the question is primarily about justice. Other

times, the concern is related to whether or not an answer is internally consistent with democracy, or

whether it actually is a paradox of founding. Only rarely however, is the link between the problem of

inclusion and the value of democracy addressed, and typically this is only ever implicit. I will show that

any instrumental account of democracy's value must be compatible with its corresponding claim of

democratic inclusion.

The second claim o!ers something new. Di!erent accounts of democracy require di!erent accounts of

inclusion. As we shall see, accounts of democracy based on content-independent criteria require

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di!erent accounts of inclusion to those based on content-relative criteria. Content-indi!erent accounts

of democracy by contrast, are compatible with a wider variety of accounts of inclusions, and are

therefore less a!ected by the Boundary Problem.

Which leads to the third claim: whenever di!ering accounts of inclusion are incompatible, their

corresponding accounts of democracy must also be incompatible. The necessary relationship between

democratic inclusion and justification means that accounts of democracy cannot be mixed if their

supporting accounts of inclusion are not compatible.

Political theorists however, frequently combine incompatible justifications of democracy. Mill as just

one example justifies democratic rule on the ground that it is more reliable in determining the right

decision (a content-independent criteria), takes into consideration the preferences of all (a content-

relative criteria), and transforms the moral character of participants (a content-indi!erent criteria).

The relationship between democratic inclusion and justification has broader implications than is

currently recognised.

To reiterate, this is not an argument about how or why the Boundary Problem is a problem for

democratic theory. The Boundary Problem raises a number of challenges for democracy but here I focus

exclusively on how it relates to instrumental accounts of democratic justification. As such, I don't seek

to explain who should be included in the demos, nor what principles might guide us to an answer.

Rather, this paper is an examination of when the Boundary Problem is a problem - of when accounts of

democratic inclusion undermine accounts of democracy's value.

― Methodology ―

How then can we examine the relationship between democratic inclusion and democratic authority?

How does changing the make up of the demos changes the outcome of democratic processes? As

philosophers, deductively reasoning from first principles or mutually agreed upon premises is a time-

honoured approach. We might first postulate some axioms of human nature and essential conditions of

democracy before then demonstrating that certain states of a!airs are necessary or possible, entailed or

contradictory. The obvious limitation with this approach however, is that many fundamental questions

of political science, theory, and philosophy, are questions of empirical fact. The biological and

psychological forces that drive human behaviour, and the conditions under which actual democracies

operate, are such that they cannot be deduced from self reflection whist sitting in a leather arm-chair.

Given the empirical nature of the investigation then, we could perhaps employ a scientific approach.

We might observe how actual democratic polities form and how di!erent compositions of polities lead

to di!erent democratic outcomes. Yet the complexity of human political systems makes causal claims

all but impossible. The lack of adequate sample sizes when using democratic states as relata, the non-

linearity that arises from multiple interacting feedback loops, and the inability to hold variables fix 'in

the wild' impose severe limits on our causal modelling and explanations that are well known to social

scientists.

But a third approach, although rarely used in philosophy, o!ers considerable insight into this problem.

Computer simulation combines advantages of both approaches. Typically, simulations are used to make

predictions about the real world. They attempt to model reality as accurately as possible before showing

how changes in inputs lead to changes in the simulation. Yet this is also the primary weakness of this

approach. How well does the simulation model reality? If the model lacks fidelity with external world,

then any inferences from the model will o!er little insight into reality. And given the empirical

challenges of modelling complex human systems discussed above, the problems of simulating political

reality look overwhelming.

An alternative approach would be to simulate theory. All theories are abstractions of reality, so

simulating theory simply formalises into code the abstractions that theorists have made for centuries.

This type of simulation can be thought of as coherence testing particular theories. By making the

assumptions and abstractions of a theory explicit in code, we can see if the predictions and claims of

the theory are entailed, or at least made probable. We can show that a theoretical model is coherent

even if we can't show that the theory's assumptions do in fact hold true in reality.

What follows in the remainder of this paper is both a description of a model of democracy as well as a

simulation of that model. It attempts to capture the key claims of instrumental accounts of democracy

and explore how changing the composition of a polity a!ects the democratic processes of that polity.

The simulation process begins by defining a simple model of democracy consisting of naive voters

populating some abstract political space. Methods of inclusion and voting are then defined. Next, three

instrumental accounts of democracy - content-independent, content-relative, and content-indi!erent -

are formalised and simulated in the model over a wide variety of parameters. Finally, the relationship

between democratic inclusion and democratic outcomes is explored by examining how di!erent

compositions of agents lead to di!erent results.

A form of literate programming, this paper embeds executable source code within the description of

the model. Simulation code is indicated by indented code blocks . The reader need not understand

the embedded code or syntax in order to understand the simulation however. The code, it's purpose,

and function will be fully explained in the surrounding text. It's presence serves to formalise the

assumptions of the model in much the same way as one might include mathematical symbolism to

formalise a proof, and to promote reproducibility and testability of the research herein.

― A Model of Democracy ―

The model comprises three distinct conceptual entities: a Political Space representing the problem

domain, Political Agents who are distributed across the space, and partitions of the space that

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group agents into political units or Polities .

An agent represents a political actor or citizen. They are simple folk who hold a single discrete value

representing a belief, preference, character trait, or virtue - right or wrong, Republican or Democrat,

chocolate or vanilla, virtuous or iniquitous. This is represented formally in code as:

class Agent constructor: (@belief) ->

Agents exist within a space which represents the problem domain. A space is constructed by specifying

a profile of how many agents hold which belief, preference, or virtue. These belief are stipulative. They

are defined at the start of the simulation and form its parameters. For example, a profile of {

'chocolate': 400, 'vanilla': 600 } would create a space with 400 agents whose preference is

chocolate and 600 whose preference is vanilla.

class Space constructor: (profile) -> @agents = [] for belief, believers of profile for n in [1..believers] @agents.push new Agent(belief)

Agents are distributed across the space in some way according to their belief. This distribution could be

perfectly uniform, with agents evenly spread across the space; or agents could be tightly clustered so

that all agents of a similar belief are grouped together.

Agents in our space will be distributed according to a cluster factor which determines the proximity of

agents holding similar beliefs with one another. A factor of 1.0 will result in a highly clustered space

with all like agents grouped together, while 0.0 will result in a uniform random distribution of agent

belief.

Space::distribute = (cluster=0.0) -> quota = @agents @agents = [] while quota.length > 0 limit = Math.round( Math.random() * quota.length * (1-cluster) ) @agents = @agents.concat quota.splice limit, 1

Spaces are partitioned into polities. A polity represents a unit of political association that holds some

degree of sovereignty regarding specific issues, such as a nation-state, province, or local council. Most

political spaces are partitioned in some way - the world is divided into countries, countries are divided

into states or provinces, states are divided into electorates etc.

How we partition a space - how we decide who will be included in which political association - forms

the crux of the Boundary Problem and there are many competing theories concerning how to partition.

Amongst accounts of democratic inclusion we find proposals to group agents according to nationality,

cultural or linguistic salience, degree of economic or social interdependence, by who is a!ected by a

policy or issue, or even to not partition at all.

While numerous accounts of inclusion exist in political theory, the combination of actual possible

partitions of any space is orders of magnitude greater. To simplify the model and remain agnostic

about particular theories of inclusion while capturing a wide variety of possible agent compositions, a

stochastic algorithm to divide the space into di!erent polities will be used to generate a random sample

of polities.

The partitioning algorithm recursively divides the largest polity of the space at a random point until

the desired number of polities have been produced - each characterised by a di!ering number and

composition of agents.

Space::partition = (k) -> @polities = [@agents] while k > 1 k = Math.min k, @agents.length polity = @polities.shift() cut = Math.floor( Math.random() * (polity.length - k) ) + 1 @polities.push polity[...cut] @polities.push polity[cut..] @polities.sort (a,b) -> b.length-a.length k-- this

Democracies make collective decisions - it's why they exist. The decision procedure for our model

democracy will be a naive majority vote by each polity on a binary issue. This is the simplest decision

mechanism to model and it will assume that agents vote sincerely and deterministically according to

their belief.

vote = (polity) -> votes = {} for agent in polity if votes.hasOwnProperty agent.belief then votes[agent.belief]++ else votes[agent.belief] = 1 max = Math.max.apply null, (num for belief, num of votes) votes.winner = belief for belief, num of votes when num is max votes

With our model now defined, the relationship between accounts of democracy and accounts of

inclusion can now be explored by running Monte Carlo simulations of the model for various

combinations of agent, clusterings, and partitions.

At the beginning of each simulation, a space is created with a fixed agent profile, clustering factor, and

polity number. During each run, the space is partitioned into the desired number of polities which then

vote, with the results being recorded for statistical analysis.

This partition-vote-measure loop is repeated 1000 times, generating in a probability density function

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of the votes in each polity for each belief-cluster-partition tuple. These results are then assessed against

three classes of instrumental accounts of democracy to examine the conditions under which accounts

of inclusion a!ect accounts of democracy.

― Content Independent Outcomes ―

One common justification for democracy is epistemic - that democracy has instrumental value as a

truth tracking processes. Some of these epistemic accounts are relatively simple and Condorcet's Jury

Theorem is one such example. Given a better-than-even chance of any voter being correct on some

choice, then the likelihood of a majority vote being being correct on that choice approaches certainty as

the number of voters increases.

Others, like Estlund 's Epistemic Proceduralism, are more nuanced. Rather than valuing democracy on

the basis of the outcome of a specific vote, democracy has legitimacy because much like a jury, its

decision processes have a tendency to produce correct decisions. Even when the majority is wrong on a

particular matter, the majority decision is still morally binding, so long as majority voting remains the

more reliable procedure than alternatives.

While di!erent, all epistemic accounts rely on the claim that democratic procedures, on average, are

better at determining the correct result than alternate ones. Further more, these results are correct

independently of the decision procedure used.

This type of justification requires some way of comparing the epistemic performance of di!erent

decision procedures and one intuitive way to do this is to assess them against some base line metric. An

obvious candidate for such a metric is the likelihood that any randomly selected voter holds the correct

belief or votes correctly - what I will call the epistemic base rate of a political space. We can then judge the

epistemic performance of a decision procedure against the epistemic base rate. Call this di!erence a

procedure's epistemic virtue.

In our simulation, the epistemic virtue of a simple majority vote can be measured as the frequency

based probability that a polity votes correctly given the initial conditions of the space. During each

trial, the number of polities that voted correctly is measured and the impact of di!ering partitions

assessed. The correct answer to the question our agents vote on is known in advance because we

stipulate it when we create agents with either right or wrong belief.

Space::virtue = () -> correctVotes = 0 for polity in @polities election = vote polity correctVotes += 1 if election.winner is 'right' correctVotes / @polities.length

Running a Monte Carlo simulation hundreds of thousands of times for a range of partition numbers (5

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to 30), cluster factors (0.0 to 1.0) and epistemic base rates (0.5 to 1.0) yields a four dimensional data cube

of probability distributions for the expected correct majority vote in each base-rate-partition-cluster

tuple.

We can examine the results from any perspective or slice of the data cube. In the graph below, we see

the impact of repartitioning on epistemic virtue at an epistemic base rate of 0.6 from the perspective of

clustering. The vertical axis represents epistemic virtue and the horizontal axis, the degree of

clustering. Each line represents the number of polities the space was partitioned into, ranging from 5 to

30 partitions.

The likelihood of any randomly selected voter in the space being correct is 0.6. When agents are

uniformly distributed across the space by belief (i.e. no clustering of agent belief is present), the

epistemic virtue of majority voting - the likelihood that the majority vote of any polity is the correct

choice - is very high (0.82-0.97). This quickly deteriorates as clustering of agent belief increases

however, with no epistemic virtue of majority voting evident once agent clustering reaches 0.5. This

holds true for all levels of partition numbers and epistemic base rates > 0.5, although the e!ect

diminishes as diversity across the space diminishes.

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Epistemic virtue by cluster factor

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Examining the same data from the perspective of partition number, we see little impact of partition

number on epistemic virtue for higher cluster factors, and only limited impact for low levels of

clustering, concordant with Condorcet's Theorem. This relationship holds for all epistemic base rates

between 0.51 and 0.99.

These results indicate that the epistemic virtue of majority voting is dependent not only on individual

agent belief having a greater than 50% likelihood of being correct, but also on how those agent beliefs

are distributed across the political space. A key stipulation of the Jury Theorem is that there must a

better than average chance of any voter being correct - we might call this the competency requirement. This

simulation shows that when clustering of agent belief is present, even if the competency requirement

is met for the space as a whole, it is not necessarily met for every partition of that space. Furthermore,

as clustering of agent belief across the space increases, the likelihood that every partition of the space

satisfies the competency criteria decreases.

The relationship between content-independent justifications of democracy and democratic inclusion is

now clearer. Epistemic justifications of democracy require accounts of inclusion that ensures that:

1. Polities are su#ciently large for the Condorcet e!ect to emerge.

2. Any partition of a space that satisfied the competency requirement must also satisfy the

competency requirement.

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Epistemic virtue by partition number

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When the distribution of voter belief is uniform, where we draw the boundaries of our democracies is

largely irrelevant for content-independent accounts of democracy. Any account of democratic

inclusion will do. But when the distribution of voter belief is clustered, where we draw boundaries of

our democracies becomes very important. In this case, any compatible account of democratic inclusion

will need to demonstrate that each polity satisfies the competency requirement for epistemic

justifications.

We can summarise this finding by stating that the Boundary Problem only becomes a problem for

content-independent justifications of democracy when homogeneity of voter belief or competence is

high within polities but low between them. In these instances, how we bound the demos and draw

political borders is critical. Content-independent justifications require accounts of inclusion that

generate su#ciently large, externally homogeneous polities. Polities needs to be large and have similar

voter composition otherwise only some of them can be justified by content-independent accounts.

― Content Relative Outcomes ―

Not all instrumental accounts of democracy are epistemic however. Utilitarians justify democracy on

the grounds that it promotes the greatest happiness. Majority voting maximises the expected utility of

voter preferences when each individual has an equal chance of preferring each of two alternatives.

But one needn't be a card carrying utilitarian to employ such an approach. Rousseau argued that

majority rule realises the general will of the people and this gives us reasons to obey, while social choice

theorists hold that majority voting realises individual choice when collectively binding decisions must

be made (Kenneth O May, ).

While these accounts of democracy di!er in many ways, they all share a similarity in that the value of

democracy stems from some content-relative criteria - of fidelity between individual preference and

collective outcomes. It is not the contents of the outcome of a democratic process that matters per se,

but rather how well this collective outcome matches the wants, preferences, or intent of individual

participants.

We can judge these content-relative outcomes by defining the fidelity of a democratic procedure as the

likelihood that an individual's preference is the same as, or compatible with, the majority outcome.

Formalising fidelity as individual-collective choice equivalence we get:

Space::fidelity = () -> winners = 0 population = 0 for polity in @polities election = vote polity for key, val of election winners += val if key is election.winner population += val unless key is 'winner' winners / population

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Running the same Monte Carlo simulation with the same parameters as the epistemic simulation yields

a di!erent set of results to those of the content-independent one. Below, we see the fidelity of

individual preference to majority vote for a distribution of agents with a 60:40 preference for some

choice A or B over a range of clustering and partition variables, viewed by degree of clustering.

Again, when viewed by degree of clustering, the e!ect of polity composition on preference realisation

is stark. When agents are uniformly distributed by preference across the space (i.e. when clustering is

low), the likelihood of an individual's preference being realised by majority vote is identical to that of

any two random agents preference being the same (i.e. the preference base rate).

As clustering of agent preferences across the space increases however, the fidelity between individual

and majority preference increases significantly. At its most extreme, there is near certainty that any

individual preference will be realised by a majority vote of a polity when the distribution of agents

across the political space is fully clustered - when agents are completely segregated by preference. This

relationship holds for all preference base rates, although it is more pronounced when the preference

base rate - the ratio of competing preferences - is lower.

In contrast with the epistemic simulation of democracy however, the impact of agent clustering on

outcome quality is reversed. Majority voting has the greatest likelihood of fidelity with individual

preference, and therefore greatest value from a content-relative perspective, when agents are highly

clustered. This contrasts sharply with the content-independent perspective where the greatest

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Preference fidelity by clustering

epistemic value of majority voting was found with a completely uniform agent distribution.

The number of polities a space is partitioned into has only a limited e!ect in individual-majority

preference fidelity. As the space is partioned into increasing numbers of polities, fidelity increases

slightly when preference are highly clustered, but the influence of partition number is significantly less

than the impact of preference clustering.

The key implication from this analysis is that accounts of democracy based on content-relative criteria

such as the fidelity of individual with group preference require an account of democratic inclusion that

ensures that:

1. Polities are su#ciently small.

2. Voters are as internally homogeneous as possible.

Restated, where we draw political boundaries is largely irrelevant for content-relative accounts of

democracy if the distribution of voters by preference is highly clustered. Just about any account of

inclusion will likely generate internally homogeneous polities. Where we draw boundaries is very

important however, when the distribution of voters by preference is uniform. The Boundary Problem

only becomes a problem for content-relative justifications of democracy when homogeneity of voter

preferences is low within polities but high between them. Content-independent justifications require

accounts of inclusion that generate su#ciently small, internally homogeneous polities.

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Preference fidelity by partition number

― Content Indi!erent Outcomes ―

A third type of instrumental justification of democracy is concerned not with the specific content of

democratic outcomes, but with their beneficial side e!ects. It is not the result of a vote or policy

deliberation that matter per se, rather it is the e!ect that democratic participation has on citizens that is

valuable. Democracy on this account is transformative.

Public life as the path to personal improvement is an idea that can be traced back to the Greeks. More

recently, Rousseau thought democracy a necessary condition for the realisation of moral autonomy:

. . . what man acquires in the civil state, moral liberty, which alone makes him truly master of himself; for

the mere impulse of appetite is slavery, while obedience to a law which we prescribe to ourselves is liberty.

For Mill, democracy was the means to improve the moral character of the people. The weighing of

di!erent people's interests, being guided by other's rules, and applying principles that advanced the

common good, enhanced a citizen's moral capacities:

Still more salutary is the moral part of the instruction afforded by the participation of the private citizen,

if even rarely, in public functions ... He is made to feel himself one of the public, and whatever is for their

benefit to be for his benefit.

We might call these types of instrumental justifications of democracy content indifferent, because it's not

the content of democratic outcomes that matters per se but rather some side e!ect of democratic

activity that matters.

One way to formalise this type of account is to stipulate that agent character improves consistently for

all citizens when they vote (or deliberate). This would model an agent-blind process in which every

voter's character improves to the same degree, regardless of how politically active they are or who they

interact with. A more plausible model however, would see agent character improve dependent on who

they interact with. Win-at-all-costs politics characterised by media manipulation and voter apathy

seem less likely to positively transform the character of participants than contests marked by honest

and open debate.

In the formalisation below, agent character improves relative to the average character of their polity,

with more virtuous polities improving their citizen's character to a greater extent than less virtuous

ones. Good eggs are assigned a random value representing moral character between 0.5 and 1.0

while bad apples are assigned one below 0.5 . Democratic activity here 'closes the gap' between an

agent's actual and maximum character potential, by a factor determined by the average character in

their polity.

Space::character = () ->

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Space::character = () -> polity_improvements = [] for polity in @polities characters = polity.map (agent) -> character = if agent.belief is 'good' then 0.5 else 0.0 character += Math.random() / 2 average_character_in_polity = ave characters gap_closed = ave characters.map (val) -> (1 - val) * average_character_in_polity + val polity_improvements.push gap_closed ave polity_improvements

When viewed from the perspective of clustering, a small e!ect on moral character is noticeable. With

little agent clustering across the space, the improvement in an agent's moral character is strong (at a

base rate of 0.6, average improvement is approximately 0.8). As clustering increases, character

improvement is less strong (0.75 for the same parameters). Unlike content-independent and content-

relative justifications in which changes in clustering can completely undermine the relevant

instrumental e!ect, the e!ect of content-indi!erent accounts is still present across all clustering levels.

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Viewed from the perspective of partition numbers, no change in moral character is observer able.

Di!erences in the transformative impact of democracy on an agent's moral character appear to be fully

dependent on the degree of clustering across the space.

While less clustering is optimal for content-indi!erent accounts of democracy, any partition of a space

will result in a positive transformative e!ect as modelled here. Any account of inclusion will do.

Content-indi!erent justifications of democracy are compatible with both content-independent and

content-relative accounts.

― Conclusion ―

The claims of some justifications of democracy are not entailed in all circumstances. How we answer

the question of who the people should be can either support or undermine these accounts. Content-

independent accounts like Condorcet's Jury Theorem are unlikely to hold true when people are highly

clustered by belief or epistemic competence. When clustering is present, democracy has no epistemic

virtue. Content-relative accounts like preference realisation by contrast, are likely to be entailed when

peoples preferences or values are evenly spread. A uniform distribution undermines claim that

democracy maximised preferences or best realises personal values. Meanwhile, content-indi!erent

accounts perform almost equally well irrespective of how people are distributed.

The implication of inclusion on instrumental justifications of democracy is clear. If we are to accept the

Base Rate 0.60

5 10 15 20 25 30partitions

0.40

0.45

0.50

0.55

0.60

0.65

0.70

0.75

0.80

0.85

0.90

0.95

1.00

mor

al c

hara

cter

Character improvement by partition number

claims of these accounts, then they must provide a corresponding and congruent account of inclusion.

The impact of voter composition on the outcomes of democratic processes places an addition

constraint upon these accounts of democracy, such that any instrumental account of democracy must

also o!er a corresponding account of inclusion.

Di!erent accounts of democracy require di!erent accounts of inclusion. As can be seen from the

simulation of the epistemic and preference realisation models, the corresponding account of inclusions

needed are incompatible. Content-independent justifications require accounts of inclusion that

generate su#ciently large, externally homogeneous, and typically, internally heterogeneous polities.

Content-independent justifications require the opposite. They require accounts of inclusion that

generate su#ciently small, internally homogeneous, and typically, externally heterogeneous polities.

These accounts of inclusion are obviously incompatible. How we answer the question of who should the

people be for one account of democracy will not be same for another account of democracy.

So if instrumental justifications of democracy require di!erent accounts of inclusion, and those

accounts of inclusion are incompatible, then certain instrumental justifications of democracy are

themselves incompatible. One simply cannot maintain that democratic authority is justified because it

has both epistemic virtue and realises individual preferences. Yet many justifications of democracy do

exactly this. Mill for example, justifies democracy on both epistemic and strategic grounds, arguing that

democratic authority is legitimate because it generally reaches good decisions and is forced to consider

the preferences of all citizens. The incompatibility of accounts of inclusion that these approaches

require however, demonstrates that this type of hybrid justification is incoherent.

Of course, this incompatibility constraint does not apply to all instrumental justifications of

democracy. Content-indi!erent justifications like Mill's moral transformation account can work with

any distribution of voter character. For content-indi!erent accounts, any account of inclusion will do.

The accounts of inclusion required by these types of justification are compatible with those required

for either content-independent or content-relative justifications. But not, however, with both.

― Appendix ―

A number of helper functions are necessary for the simulation to work as an independent program. As

these are not germane to the central argument, the have been extracted from the paper's body to here.

First let's define some simple statistical functions.

sum = (arr) -> arr.reduce (a,b) -> a + bave = (arr) -> sum(arr) / arr.lengthvariance = (arr) -> mean = ave(arr) (arr.reduce ( (a,b) -> a + (mean-b)*(mean-b)), 0) / arr.lengthstdev = (arr) -> Math.sqrt( variance arr)

Next, we need to run the simulation. The following function runs a simulation for the given parameters

and number of trials.

simulateDemocracy = (account, agents, partitions, clustering, trials) -> space = new Space agents space.distribute clustering results = { 'a': agents, 'p': partitions, 'c': clustering, 'trials': [] } for trial in [1..trials] results.trials.push space[account]( space.partition partitions ) results

The results now need to be saved. We'll save them in to a local file in JSON format for ease of

consumption later on.

fs = require 'fs'save = (name, results) -> fs.writeFile "assets/#{name}.json", JSON.stringify(results) , (err) -> if err then console.log err

Now we need to bootstrap the simulation. We run it by assigning a name, metric, and some choices for

the agents to vote on.

runSimulation = (name, metric, choices) -> bases = [0..10] partitions = [1..6] clusters = [0..10] results = []

for b in bases b = 500 + b*50 for p in partitions p = p * 5 for c in clusters c = c / 10 sim = simulateDemocracy metric, {"#{choices[0]}": b, "#{choices[1]}": 1000-b}, p, c, 1000 results.push { "baserate": b, "partitions": p, "clustering": c.toFixed(2), "#{name} #{metric}": ave(sim.trials).toFixed(15) } process.stdout.write "Running #{results.length * 1000} #{name} trials\r" save name, results

Finally, we capture terminal inputs to start up the simulation. To run the simulation of epistemic

democracy, use the command coffee paper.coffee.md epistemic . This will execute the code

embedded described in the paper above.

process.argv.forEach (val, index, array) -> runSimulation('epistemic', 'virtue', ['right', 'wrong']) if val is 'epistemic' runSimulation('preference', 'fidelity', ['red', 'blue']) if val is 'preference' runSimulation('moral', 'character', ['good', 'bad']) if val is 'character'

1. The term justification has been used in a variety of ways within political theory. Sometimes it is

used normatively to describe the content of reasons that might legitimate democratic authority.

Other times it is used descriptively to to describe the giving of such reasons. In this paper I use

justifications of democracy and accounts of democracy synonymously to mean any normative theory of

democracy's value.↩2. Marquis de Condorcet, ‘Essay on the application of mathematics to the theory of decision-

making’, Reprinted in Condorcet: Selected Writings, Keith Michael Baker, ed 33 (1976). ↩3. David M Estlund, Democratic Authority: A Philosophical Framework (Princeton University Press,

2009). ↩4. Douglas W Rae, ‘Decision-rules and individual values in constitutional choice’, American Political

Science Review 63, 01 (1969): 40–56. ↩5. The Social Contract: & Discourses (JM Dent & sons, Limited, 1920).↩6. Considerations on Representative Govrnment, 1862.↩7. Of course not all accounts of democracy are instrumental. Sometimes democracy is justified

intrinsically by appealing to substantive ideals like equality or justice. Unless explicitly stated,

democracy in this paper refers exclusively those instrumental conceptions where outcomes do the

normative of explaining democracy's value.↩8. Timothy Feddersen and Wolfgang Pesendorfer, ‘Elections, information aggregation, and strategic

voting’, Proceedings of the National Academy of Sciences 96, 19 (1999): 10572–4. ↩9. The Boundary Problem of Democratic Theory has gone by a number of names in political theory.

Robert Alan Dahl, , Democracy and Its Critics (Yale University Press, 1989), p. 193 has called it "the

problem of the unit" while R.E. Goodin, , ‘Enfranchising all a!ected interests, and its

alternatives’, Philosophy & public affairs 35, 1 (2007): 40–68, at p. 42 refers to it as the problem of

"constituting the demos". Most other theorists have settled on "the Boundary Problem".↩10. See F.G. Whelan, , ‘Prologue: Democratic theory and the boundary problem’, Liberal democracy 25

(1983) for the seminal analysis of the challenges that the Boundary Problem presents as well as

more recent work by Dahl, op. cit, Gustaf Arrhenius, , ‘The boundary problem in democratic

theory’, Democracy Unbound: Basic Explorations I, 2005: 14–28, Lars Bergström, , ‘Democracy and

political boundaries’, The Viability and desirability of global democracy, Stockholm Studies in Democratic

Theory 3 (2007): 14–32, Goodin, op. cit, David Miller, , ‘Democracy’s domain’, Philosophy & public

affairs 37, 3 (2009): 201–28, Hans Agné, , ‘Why democracy must be global: Self-founding and

democratic intervention’, International Theory 2, 03 (2010): 381–409, Arash Abizadeh, , ‘On the

demos and its kin: Nationalism, democracy, and the boundary problem’, American Political Science

Review 106, 04 (2012): 867–82, Johan Karlsson Scha!er, , ‘The boundaries of transnational

democracy: Alternatives to the all-a!ected principle’, Review of International Studies 38, 2 (2012):

321–42, Sarah Song, , ‘The boundary problem in democratic theory: Why the demos should be

bounded by the state’, International Theory 4, 1 (2012): 39–68, and Eva Erman, , ‘The boundary

problem and the ideal of democracy’, Constellations 21, 4 (2014): 535–46

<http://dx.doi.org/10.1111/1467-8675.12116>.↩

11. Arrhenius op. cit. p1. ↩12. Whelan op. cit. p13. ↩13. Robert Alan Dahl, After the Revolution?: Authority in a Good Society (Yale University Press, 1970)

<http://books.google.com.au/books?id=5ENQAQAAIAAJ> pp59-60. ↩14. See Goodin, op. cit, Agné, op. cit, Abizadeh, op. cit, Ben Saunders, , ‘The democratic turnout

“problem”’, Political Studies 60, 2 (2012): 306–20, and Erman, op. cit for arguments from the

cosmopolitan perspective.↩15. See Whelan, op. cit, Arrhenius, op. cit, Bergström, op. cit, Miller, op. cit, Scha!er, op. cit, Song, op.

cit, and Paulina Ochoa Espejo, , ‘People, territory, and legitimacy in democratic states’, American

Journal of Political Science 58, 2 (2014): 466–78 for work concerned with how the Boundary Problem

a!ects democratic legitimacy and territorial states.↩16. Literate programming is a paradigm of computer programming that explains the logic of a

system in essay like form, interspersed with snippets of source code that a compiler executes. The

aim is to prioritise human understanding of the program logic over compiler e#ciency. See

Donald Ervin Knuth, , ‘Literate programming’, The Computer Journal 27, 2 (1984): 97–111 for an

introduction to the topic.↩17. As Goodin, op. cit. , p.55 observes, "Virtually (maybe literally) everyone in the world — and indeed

everyone in all possible future worlds — should be entitled to vote on any proposal or any

proposal for proposals".↩18. The possible number of di!erent partitions is the sum of binomial coe#cients of agents and the

number groups they are partitioned into. This increases exponentially as the number of agents

and groups increases, making a simulating all possible partitions within a reasonable time frame

is beyond the capacity of current desktop computing.↩19. Monte Carlo simulations are class of computational algorithms that rely on statistical sampling

from repeated simulation trials to generate numerical results. see George S Fishman, Monte Carlo:

Concepts, Algorithms, and Applications (Springer, 1996) for a full treatment of their use in computer

simulation.↩20. See Christin List and Robert E Goodin, ‘Epistemic democracy: Generalizing the condorcet jury

theorem’, Journal of Political Philosophy 9, 3 (2001): 277–306. ↩21. op. cit.↩22. A general principle about polity likeness is observable. For any given distribution of agents across

a space, the more internally homogeneous a polity is, them more externally heterogeneous it

must be, and vice versa. This is most pronounced when agent diversity within the space is high,

i.e. when epistemic or preference base rates are close to 0.5, but the relationship deceases as the

diversity in the decreases, i.e. when the base rates approach 0.0 or 1.0.↩23. Condorcet's Jury Theorem posits that the likelihood of majority rule selecting the correct

outcome increases as the number of voters increases (assuming voters have an independent

better than even chance of voting correctly). We should expect to see a gradual decrease in

epistemic virtue as the same number of voters in the space are partitioned into increasing

numbers of polities.↩24. Rae op. cit. ↩25. op. cit.↩26. ‘A set of independent necessary and su#cient conditions for simple majority decision’,

Econometrica: Journal of the Econometric Society, 1952: 680–4.↩27. op. cit. , sec.1.8.3.↩28. op. cit. Ch 3.↩29. Content indi!erent justifications are not typically used in isolation. Both Mill and Rousseau used

these content indi!erent justifications in conjunction with other instrumental justifications of

democracy such as strategic value, truth divination, and preference articulation.↩