Thursday, January 05, 2006

Lottery Voting: An Introduction

I spent most of yesterday (well, most of yesterday afternoon, which was all the work I did...) writing the following piece, for the Warwick Political Theory Graduate Conference next month, so here it is (for next time someone asks what my PhD is on):

Since twenty minutes isn’t much time to get into detailed argument, and such specifics are generally hard to follow without an idea of the overall argument, I intend to provide what’s largely just a sketch of my wider PhD thesis. This is helpful also because, although it’s based on my M.Phil thesis, I’m only now expanding the project, so questions on any area will help me see what needs to be addressed further.

The aim of my thesis is to argue for a new, non-majoritarian form of democracy – something I call ‘lottery-voting’. The name in fact comes from Akhil Amar, who wrote two articles[1] advocating such a process. As radical as it seems, it’s by no means an original idea. It’s also discussed – though not necessarily endorsed – by Bruce Ackerman, Robert Paul Wolff, David Estlund and Paul Jones[2]. The novelty shall come, I hope, in my argument for it.

Since I won’t assume familiarity with the idea, I’ll begin by spelling it out. The proposal is that elections are held as at present, but instead of votes being counted up and the side with most votes winning, one vote is drawn at random to determine the result. This is sometimes known as ‘random dictator’, for an arbitrarily chosen person is taken to decide the outcome, regardless of everyone else’s votes.

This means each person’s vote has an equal chance of affecting (in fact, deciding) the outcome – because every vote has an equal probability of being drawn. Overall, the result will be that side A in the contest has a probability of winning the vote equal to the proportion of people who vote for A. Thus, if one side wins 60% of the votes, then they have a 60% chance of winning – because there is a 60% chance of one of these votes being randomly drawn. If the other side took the other 40% of the votes, however, they still have a 40% chance of winning. Therefore proportionality is preserved up until this stage, though once one vote is drawn the ‘winner takes all’ – i.e. the decision goes wholly that way, there is no further compromise when it comes to the actual policy implemented.

Of course, the fairness of this procedure will need defending at length, and that’s what my thesis sets out to do. Whereas Amar only puts forward the idea as a ‘thought experiment’, and then considers its consequences, I intend to argue to such a proposal, from fundamental accounts of equality and the fairness of lotteries, and then assess its workability.

One might wonder, for example, whether it’s fair that one side has a 60% chance and the other only 40% – it means some people will have a far greater expectation of getting their way. This is why Wolff rejects the proposal – “legislation by lot would offer some chance to the minority, unlike rule by the majority, but it would not offer to each citizen an equal chance that his preference be enacted”[3] because a side with more supporters will have a greater chance of winning. However, I argue this follows from treating each person equally – what groups get is proportional. If we want some form of collective decision-making, then assuming a lack of unanimity, there will inevitably be winners and losers. The question is a distributive one – who is to be satisfied and who not.

Although lottery-voting mean that some people benefit in effect from the good luck of others, I think this is a consequence we can and should accept – it’s something we often see, for example, in markets. Further, I believe more people count for more, what lottery-voting does is restrict their influence to what’s proportional to their numbers. In this respect, it’s certainly better than majority-rule, where the 60% are guaranteed to get all their way. The alternative would be to give every option an equal chance, so even where voters were split 60/40 between two alternatives what we should do effectively is toss a coin between them. However, this assumes that options are defined in advance, and if that’s so then it completely ignores people’s votes. It might be defended as a form of fair division, but certainly not as democratic.

It will be clear that I think of democracy as a distributional issue, in which case there is a connection between majority-rule and utilitarianism, since both could be said to produce the ‘greatest happiness of the greatest number’. This is brought out by Nagel, who says “The moral equality of utilitarianism is a kind of majority rule: each person’s interests count once, but some may be outweighed by others… the basic idea is majoritarian because each individual is accorded the same (variable) weight and the outcome is determined by the largest total”[4]. In fact, however, this also highlights how majority-rule is imperfect as a mechanism for delivering utilitarian-optimal outcomes. When it comes to decision-making, we have to treat each equally – ‘one person, one vote’ – but utilitarianism should be sensitive to intensity of preference – the few should be able to override the many if the quantity of their happiness is greater. It’s only by denying any possibility of comparison that we could arrive at the crude equality assumed in ordinary majority-rule procedures, yet it seems quite obvious that we can make some comparisons – two people who risk a sore throat should not be able to out-vote one who risks losing his legs, as their claims are intuitively unequal.

Majority-rule can be defended as an account of fairness if we assume no one knows where they will end up – that is, as something that would be agreed to in some hypothetical contract situation. In this situation, however, ‘fairness’ seems highly indeterminate. Since no one knows where they’re likely to be, they could seemingly adopt any rule – the majority decides, the minority decides, the side with the most redheads wins, always preserve the status quo, the oldest person decides… All of these seem fair because they don’t have any a priori bias in favour of particular people. What recommends majority-rule is a combination of fairness and the intuitively attractive idea that it’s usually better to satisfy more people than fewer. From this perspective, it seems everyone would accept majority-rule, reasoning they have more chance of being in the majority than any other group.

The hypothetical contract situation assumed here, however, is one in which contractors assume they have an equal chance of occupying any position in society, and thus a greater chance of being in the majority. This is the assumption John Harsanyi uses to argue for utilitarianism, on the grounds that everyone maximises their expected utility by agreeing for society to maximise average utility[5]. Not everyone accepts these assumptions, however. For instance, Rawls’ famous Original Position denies parties knowledge of probabilities, thus contractors wouldn’t be able to assume that they were any more likely of being in the majority group than any other group. In this case, there’s nothing they can do to maximise their own chance of being satisfied. One central motivation of my project, therefore, is the belief that a consistent Rawlsian should reject majority-rule for the same reason as he rejects utilitarianism.

But Rawls in fact has a different argument for majority-rule, which seems to rely on an epistemic case for democracy: the assumption that a majority are more likely to be right. He claims, “the political process is a case of imperfect procedural justice”[6], that is, a case in which a group of people are reasoning about an issue to which there is, in principle, an objectively right answer, as in a jury trial. If this is so, and we assume each individual is more likely to reach the right answer, then Condorcet’s Jury Theorem tells us that a majority is much more likely to be reliable.

I’m sceptical about the epistemic case, however. Firstly, Condorcet’s Jury Theorem makes a number of questionable assumptions, such as a binary choice, that individuals are more likely right than wrong, and independence of judgements. Secondly, I am a value pluralist, and do not believe in uniquely right answers.

Part of the reason I see democracy as a struggle over the distribution of good is that I think there is good-for-x and good-for-y, but I’m wary of something like an impartial or ‘common’ good above that. Utilitarians accept the aggregation of good across individuals, as if the greater good x gains somehow compensates y for a loss. Fundamental to Rawls, however, is the ‘separateness of persons’, thus he says, “Each person possesses an inviolability founded on justice that even the welfare of society as a whole cannot override… It does not allow that the sacrifices imposed on a few are outweighed by the larger sum of advantages enjoyed by many”[7]. Person y does not forfeit her claim just because w and x together stand to gain more, for that would be to ignore their separateness and “to adopt for society as a whole the principle of rational choice for one man”[8].

While majority-rule may indeed be fair if people’s political positions and coalitions aren’t fixed in advance – that is, if voters are effectively randomly assigned to options. In actual fact, however, this is rarely the case. To people with known and fixed identities, the problem of permanent minorities arises. The hypothetical fact they could have been in the majority, had they been someone else, is unlikely to appease them. What we need is a procedure that no one could reasonably reject, and I think lottery-voting offers this. Every vote is intuitively equal, and each group stands a proportional chance of having its way. Admittedly this still means some are more likely to be satisfied than others, but that is in accordance to the numbers they can win to support their side. Thus lottery-voting fosters democratic values such as deliberation and persuasion. Because every vote is equal, there will no longer be such thing as ‘safe seats’. Rather all votes matter, and any party can increase its chances of winning by persuading more voters. Thus there are incentives for minorities to try to reach 30% rather than 20%, say, and conversely no party can rest safe even with 70% support – it’d be better to win 80%.

Of course, it is a consequence that fewer people will sometimes have their claims satisfied rather than more, but I do not think this itself is an objection – it is simply respecting those people equally that means they get a proportional weight too. I have denied that this is in any sense ‘impersonally worse’ – it is worse for those who do not get their way, of course, but better for the minority concerned. Further it seems fair that over the long run of the political process, a consistent 30% of the voters could expect their way on about 30% of the legislation. Compromise thus comes over the whole, rather than each part.

The whole thesis, of course, has – or rather, will have – much more on procedural versus outcome-based understandings of democracy, arguments against majority-rule, fairness of lotteries, rationality and social choice and practical implementation, but this presents the main ideas and motivations.

[1]A. R. Amar (1984) ‘Choosing Representatives by Lottery Voting’ The Yale Law Journal 93 1283-1308 and (1995) ‘Lottery Voting: A Thought Experiment’ University of Chicago Legal Forum 193-204
[2] B. Ackerman (1980) Social Justice in the Liberal State (New Haven: Yale UP) p.288; R. P. Wolff (1976) In Defense of Anarchism (New York: Harper & Row) p.45; D. Estlund (1997) ‘Beyond Fairness and Deliberation: The Epistemic Dimension of Democratic Authority’ in J. Bohman and W. Rehg (eds.) (1997) Deliberative Democracy: Essays on reason and politics (Cambridge, Mass.: MIT) p.193; P. Jones (1983) ‘Political Equality and Majority Rule’ in D. Miller and L. Siedentop (eds.) (1983) The Nature of Political Theory (Oxford: Clarendon) p.??.
[3] R. P. Wolff (1976) In Defense of Anarchism (New York: Harper & Row) p.45.
[4] T. Nagel (1977) ‘Equality’ in M. Clayton and A. Williams (eds.) (2000) The Ideal of Equality (Basingstoke: Palgrave Macmillan) p.65.
[5] Harsanyi (1953) ‘Cardinal Utility in Welfare Economics and in the Theory of Risk-Taking’ The Journal of Political Economy 61:5 434-5
[6] Rawls (1999) A Theory of Justice. Revised Edition p.201.
[7] Rawls (1999) A Theory of Justice. Revised Edition p.3.
[8] Rawls (1999) A Theory of Justice. Revised Edition p.24.


  1. The problem with majority rule in a 2 alternative election is just that there are only 2 alternatives. The goal should be to increase the number of alternatives with different outcomes applying, if possible, to different minorities. For example, in proportional representation each minority wins in a sense since each minority gets a percentage of seats equal to its percentage of the whole population.

    The utilitarian solution would be for each minority to get its first choice if possible. Then measuring happiness in terms of what choice in her list of alternatives each person gets, this would mean total happiness for the entire population. If there are constraints such that each person cannot get their #1 choice, then some people might have to settle for choices somewhere down their preference list and society as a whole would be less than perfectly happy. However, if these choices(by society) are made such as to maximize the utility of society as a whole,and then, subject to that condition, assuming there are many tied outcomes, choosing a solution that minimizes inequality, you have a very utilitarian outcome or outcomes. Please see my website href="" for more.

  2. thanks so much for this articulate article :)