Saturday, February 14, 2009

Chancy Elections

What is the best electoral process? Universal suffrage and 'one person, one vote' seems like a good start. But granting that, there's a further question, namely, what to do with all those votes. Our present 'majoritarian' system simply tallies the votes, and awards the election to whoever receives the most. Consider an alternative that Jack and I have been thinking about: use the votes as the basis of a lottery. A randomly chosen vote then determines the outcome of the election.

As stated, this sounds too risky. (If 1% of the population votes for fringe nutters, we wouldn't want to be landed with a 1% chance of a fringe nutter becoming president.) But, as Jack pointed out to me, there's an easy solution: let each vote transform into n lottery tickets, and keep randomly drawing tickets until we have n for a single candidate, who is thereby declared the winner. As n increases, this exponentially reduces the risk of any single voter's (or small minority's) preferences deciding the outcome. That is, for large n, this lottery system comes to approximate our present system of guaranteeing the election to whoever receives more votes. Of course, that would defeat the whole purpose of the proposal. But we can ask what an appropriate balance of randomness would be. Let me now argue the case for introducing some degree of chance (and so perhaps preferring a low-to-moderate n -- maybe just n=2, even).

The current system exhibits a sharp 'critical level' (e.g. "50% +1", for a two-party race). Everything hangs on increasing one's vote share to this critical level, e.g. from 49.9 to 50.1. Further increases -- e.g. from 50.1% to 60% -- don't matter in the slightest for determining the election's outcome. Nor do increases that fall short of this mark: third party candidates have no real chance, and even if they increase their vote share from 1% to 10%, this doesn't do them any good. This system thus gives candidates a strong incentive to gamble: 30% of the vote share is worthless (in a 2-way race), so if an irresponsible gimmick offers some non-zero chance of doubling their popularity, this may well be worth it for them, even if they're far more likely to end up (deservedly) losing their base of support. This seems undesirable: better to have risky elections than risky candidates, we may think.

Chancy elections would mean that every vote makes a difference. Even if a candidate is way ahead (or behind) in the polls, a mere majority is no guarantee: each extra vote would contribute to making their victory more likely still. Incumbents and popular politicians could no longer risk complacency, but would instead have an incentive to pursue every single extra vote that they possibly can (without writing off those that they already have). Third party candidates could no longer be written off. A major source of voter apathy and low turnout would be averted. In sum, elections would be made more competitive.

The risk, of course, is that misfortune may deliver an election to a less popular candidate. But it may be worth tolerating some (slight) risk of this in order to obtain the benefits listed above. What do you think? (Any political theorists out there know whether this has been discussed much before?)


  1. I (unlike everybody else, I think) don't see any need to better accommodate third parties.

    Anybody who's thinking of running a third party candidacy should realize that there's a much easier path to their goal -- take your bloc of voters into a major-party primary. If you've got enough voters to win a general election, you've got way more than enough to win a primary and take over a major party. So just do that. So I don't see that any reforms should be aimed at that desideratum.

  2. I very much doubt that it would be 'easy' to take a bloc of the sort of voters who typically vote third party into a major-party primary. Nor is it easy to 'take over' major parties; in the past this has always led to temporary or permanent splitting (the Democrats formed in something like this way from one wing of the Democratic-Republicans, for example), which would put us back into third-party land. And in fact, history suggests that the easiest thing to do is not to work within a party but cannibalize its votes (the Republicans, the only fully successful third party in U.S. history, formed by killing the other wing of the Democratic-Republicans; and most of the lesser successes have occurred in this way). Working within a party is a good way to lose momentum and dissolve.

  3. Neil - in principle, primary elections are no less susceptible to the third-candidate problem.

    Suppose there are two entrenched candidates that are generally expected to be the "frontrunners", plus a third candidate that everyone actually prefers but (due to the aforementioned expectations) considers it a "waste" to vote for. Then we might end up with the pareto inoptimal outcome of each person holding their nose and voting for the entrenched candidate they hate less, rather than the newcomer everyone would actually prefer.

    My proposal might help prevent this sort of situation, since a vote for an expected "third" candidate isn't a waste after all.

    (And then there are the other benefits I mentioned, which are probably more significant in practice anyhow...)

  4. I suspect you're talking about presidential elections here; but, if not: why not some form of proportional representation?

    When it comes to presidential elections, why not instant runoff voting?

    I suppose I'm missing why this lottery system is preferable to one of the various alternative vote-counting schemes available.

  5. IRV solves the third-candidate problem, but not the arbitrary 'critical level' discussed in the main post. So the lottery scheme does more to encourage competition even in (what would otherwise be) "safe seats", for example.

  6. I'm not sure about that. I see what you're saying about the critical level, but IRV seems sufficiently unpredictable that even safe seats would require some careful watching (unless they were very safe).

    That said, what about a proportional representation system, such as single transferrable vote? By definition, (almost) every vote goes towards electing someone. It's even possible to use that system in a presidential election -- something I learned only a few minutes ago; India does this.

  7. If 1% of the population votes for fringe nutters, we wouldn't want to be landed with a 1% chance of a fringe nutter becoming president.

    If %1 of the population votes for fringe nutters, %1 of us would want to be landed with a %1 chance of a fringe nutter becoming president.

  8. As for your question of whether this has been discussed, Akil Reed Amar (currently a professor at Yale Law School) defended this idea (though just for n=1) in a note for the Yale Law Journal when he was a law student there. It won the faculty award for best student note. The note is available on his webpage, here:

    I know about it because I did collegiate debate, and it was actually a somewhat popular case in the American Parliamentary Debate Association. I don't know if it's been taken up by others in the law or polisci literature, but I can say that I never heard of any interesting, attractive principled arguments against it on the debate circuit.

  9. You might want to look at the literature on Taurek's paper on the principle of saving the greater number: the issues here and there seem to be parallel.

    I think Ben Saunders at Oxford works on this topic. A google confirms:


  10. Fascinating. I don't have a considered opinion on this argument, but I will have to think about it further. I am, however, immediately reminded of an argument put forward by a former colleague of mine. Former colleague says that we should constitute the legislature entirely by lottery. The legislature is chosen like a jury. There are n seats (former colleague would choose 2,000) and you randomly select individuals for short terms, say one year, subject to very minimal qualifications. The legislature is unicameral and has all the power (i.e., more or less a parliamentary system), subject, if you like, to a Bill of Rights and judicial review.

  11. Brandon, party takeovers are happening all the time around us. Feminists piled into the Democratic Party in the 70s and 80s and turned it into a pro-choice institution, just as the old segregationists piled into the GOP and turned it into a vehicle for opposition to minority rights. (The feminists never had a third party, the segregationists did, so it works either way.) The reinvention of parties as they absorb burgeoning interest groups is a constant process in American politics.

    You know, Richard, chancy elections in primaries actually might go well with a 2-party system. If the chancy system ends up giving one party a completely nutty candidate, at least you've got another party to vote for.

  12. Neil,

    That seems to be an extraordinarily optimistic view, and the Democratic party is a good example of why, because there was never a 'party take-over' -- not by the feminists, not by the unions, not by civil rights groups; all we have is very standard, ordinary party politics where, for instance, conservative black evangelicals have to compromise on non-racial issues that interest them, feminists have to pull back on feminist initiatives, etc., etc., in order to guarantee that a handful of the things that they've prioritized make it into the aims of the cobbled-together alliance that constitutes the party. (The Republican party is much the same way.) Being able to negotiate one or two things into the party platform, or consolidating a voting bloc within a party that's large enough that you get tossed bones, is very different from a party take-over. (And that's precisely one of the reasons why people go third party, even at the cost of losing some overall leverage.)

  13. Brandon, I really don't see the noninstrumental value of having one party that reflects your views on the whole range of issues. And it only has instrumental value if that party is politically powerful, but a party reflecting each set of preferences can't be powerful. (On contentious issues, somebody has to lose, after all.) So the plight of the conservative black evangelical doesn't bug me that much. In a big multiparty system, he could have his own miniscule party that everybody ignored. I don't think that would be a great gain for him.

    Probably the best example of recent party takeover is the takeover of the Democratic party by Iraq War opponents. After lots of frustration with their party leadership, they showed up in the primary and got the Democrats to nominate a guy who opposed the war from the beginning. Now he's going to get the troops out of Iraq. Worked perfectly well for them (by which I mean, us, I think).

  14. A colleague of mine, Ben Saunders has thought extensively about this and wrote his DPhil thesis on the topic:

    You can also try searching for the term "Random dictator" which is sometimes used to describe the system (or group of systems really).

    A couple of additional points:

    1) You say that everyone's vote counts. More accurately everyone's vote counts ex-ante, and exactly one vote counts ex-post. In a majoritarian election, votes also count ex-ante because there is a small chance that you will win by a single vote (or force a recount that leads to this...) and in that case 50%+1 of the votes count ex-post -- otherwise no votes count ex-post.

    2) A more relevant issue is how much everyone's votes count ex-ante. I did some maths on this with Ben a few years ago and it is easy to see that the degree to which your vote counts in your system is inversely proportional to the number of people voting the same way (your vote counts only if were you to not have voted the other guys would have got in). Also, it is quite possible for people's votes to count more ex-ante in majoritarian cases than in randomised cases if the vote is expected to be very close, and vastly less if it is expected to not be close.

    Overall, I think that these randomised systems are very interesting and that they are particularly interesting when considering the rational bargaining that would go on before the platforms were determined. These systems definitely give small parties (and thus minorities) more power than they have in majority-rule democracy, but it is not always clear that this is a good thing. For example, would the effects of the extremely bad groups (eg Fascists) outweigh those of the extremely good groups? This is a key practical question, even if it doesn't weigh into the question about whether this would be a more democratic system.

  15. Neil,

    I'm wondering about the sort of "political power" you're talking about here. In Canada right now, we have a minority government at the federal level, meaning no one party has enough votes to pass anything on its own. However, we also have no formal coalition, forcing the governing party to negotiate with some combination of other parties in order to get things passed. In that kind of situation, everyone's got at least some power, even very small and narrow parties (e.g., the separatist Bloc Quebecois, who only field candidates in one province). So, I don't think you're taking into account the effect a third party might have on a congress or parliament, i.e., forcing the plurality party to concede on some issues by holding the balance of power.


    But what if people want the fascist party in power? I'm not saying they should, but if they want it, shouldn't the government reflect that?

  16. Thanks for the references, all.

    ADHR - no, fascists should not have power, even if (many) people want it. Why would you think otherwise?

    Toby - it seems to me there's an important difference between the kind of ex ante efficacy votes have in ordinary majoritarianism vs. my system. The former seems merely epistemic, so that given how everyone actually voted, it turns out my vote doesn't have any real impact on the process. In the lottery case, my vote has an efficacy that goes beyond the merely epistemic fact that I couldn't have known beforehand that the critical threshold would be reached even without my vote. No, even given how everyone actually votes, the addition of my vote does something important: it (very slightly) raises the chances that my candidate will be selected in the lottery.

    I can see that you've identified a couple of senses in which one might say that votes in a lottery system "count" just the same as votes in a majoritarian system. But you've neglected the sense in which there is a real difference, and I think it is this third sense that a lot of people intuitively care about. Even if they end up "losing" the lottery, they will not feel their vote was "wasted" the way they would in almost every majoritarian election. For they really did raise their candidate's chances, in some more objective sense than is found in the majoritarian case.

  17. Neil,

    The issue really isn't having a party that reflects your views on the whole range of issues; that virtually guarantees a party of one, or at most of small groups. But the Democratic party is not a Labor party; it is not a Feminist party; and so on through the range of groups. And this means that no issue has a stable position at the table except for purely extrinsic reasons: what counts as the Democratic party platform, and as Democratic principles, is determined not on the basis of what is important for the groups it represents de facto but on the basis of what is important for the realpolitik of winning elections. This is, by the way, part of the reason why the Republican party shifted from being the de facto progressive civil rights party; party principle shifted in a series of miscalculations about how to win elections.

    Thus what we see in what you optimistically call the "takeover of the Democratic party by Iraq War proponents" is simply the tossing of some bones to an important voting bloc by Democratic politicians (in most cases exactly the same politicians!) Had Bush, by some miracle, suddenly made massive progress in terms of reasonable goals in the run-up to the election, this sudden leverage by Iraq War opponents would have dissipated as politicians (the same politicians!) shifted to focus on points where it would be easier to grab voters. But it would have had to have been a miracle; thus it was a sure thing; thus people seized on it as a point where the Republicans were vulnerable. There was no take-over; purely extrinsic factors favored an increase in political leverage on the part of war opponents.

    In a system where conservative black evangelicals had their own party (and lots of other groups had their party), coalition realpolitik would take place at the level of government, thus allowing CBE's to be more focused and united on issues of interest to their demographic while bringing all the compromise out into the open (and likewise making it clear how much the government actually represents anyone, regardless of how many people voted for them -- it's much harder to make up things about 'mandates from the people' or to pretend that parties like Republicans or Democrats are particularly good at representing the people that vote Republican or Democrat). ADHR is right about the immense potential for this in a place like Canada. And even Canada is a system closer to American two-party politics in the sense that it has traditional majority governments and near-majority governments easy to build; most other parliamentary systems allowing coalition governments are much more coalition-based.

  18. Richard,

    Why would you think otherwise?

    There's two different points here. First, we can agree that it would be a bad thing if fascists had power. (Speaking for myself, I think it would be a bad thing if conservatives had power.) However, second, it doesn't follow from that that fascists should be prohibited from taking power if they have significant voter support.

    Whether you accept this distinction depends on what you want from democracy. If you want democracy to yield the best possible government, then you won't accept it. However, if you want democracy to yield the best possible government, then you need to explain why we bother with democracy at all. Surely a benevolent tyranny would be better, if for no other reason than because it is much more efficient. Elections and the various bits of social machinery associated with democracy seem to be an elaborate waste of time if the point is to generate a good government.

    On the other hand, if you want democracy to yield a government that is legitimate because consented to by the governed, then you pretty much have to accept the above distinction. That is, if you think democracy is important because voter choice is important (this could be on a simple Lockean ground, i.e., that people have the right to govern themselves and others can govern them only through the choice of the governed), then the government we get through an election should be one that the voters have selected -- even if the voters' choices are really poor.

    As Mill put it (in a different context), you can urge, entreat, cajole, persuade, etc, etc, people not to elect a fascist government, but what is the basis for having an election in which some options are taken off the table regardless of the choice of the electorate?

  19. Richard,

    It is true that there is some extra sense in which votes count ex ante in the randomised method. The difference is that it is objectively ex ante (ie ex ante with the objective probabilities) as well as being subjectively ex ante, whereas the deterministic system is only subjectively ex ante. However, there remain two questions:

    1) Do objective probabilities matter non-instrumentally here? I really don't think so. Firstly, it is not like we are talking quantum randomness -- we are presumably talking about a situation that is basically deterministic but with unknown initial conditions (like a lottery) and I really don't see how this could be morally relevant compared to another 'non-random' system with equally unpredictable behaviour and the same statistical distributions etc. If you think this is a reason to bring in QM, then I think that is even more bizarre.

    2) Even if it is not intrinsically better, would it make voters (irrationally) feel like there vote counted in a different way? I think it probably would, but I don't see this as much of an advantage at all.

  20. Toby - I'd just tie it back to the instrumental benefits suggested in the main post. If voters care about objective probabilities then the lottery method could increase turnout, which might be a good thing. It could also lead to less "strategic" voting (if they're not worried about a vote for their genuine first preference being "wasted"), which strikes me as likely to be for the best. From the perspective of politicians, I guess your 'subjective ex ante' probabilities are what matter, but the lottery system may still create more incentive to continue to win over voters even in not-so-close contests. (At the cost of less incentive, perhaps, in the very closest contests.)

    ADHR - "you need to explain why we bother with democracy at all". That's easy: anything else is worse. (We can't institute 'benevolence'. The expected value of instituting tyranny is not good.)

    Anyway, I didn't say anyone "should be prohibited from taking power". (Many things that ought not to happen nevertheless ought not to be prohibited.) The claim was merely that we have some reason to prefer a system (e.g. majoritarianism) that makes it less likely that fascists or other dangerous fringe groups could end up with significant power. Whether the benefits of having more good small parties outweighs this risk is, as Toby says, a practical question. (I'm used to pretty decent small parties in New Zealand, but other countries might be worse in this respect.)

    Aside: "if you want democracy to yield a government that is legitimate because consented to by the governed... then the government we get through an election should be one that the voters have selected"

    Not necessarily. There's no meaningful sense in which a sectarian government elected by a [civically disrespectful] majority faction has the "consent" of the governed minority. But this is off-topic. See my paper on democracy for more. (You're welcome to continue the discussion there.)

  21. I thank those who've already plugged my doctoral thesis.

    Someone's already mentioned Amar, who's actually written two articles:

    A. R. Amar (1984) ‘Choosing Representatives by Lottery Voting’ The Yale Law Journal 93 1283-1308

    A. R. Amar (1995) ‘Lottery Voting: A Thought Experiment’ University of Chicago Legal Forum 193-204

    Those are the only sustained treatments of such an idea, bar my thesis, to my knowledge. It does come up briefly in a few other places, however:

    B. Ackerman (1980) Social Justice in the Liberal State (New Haven: Yale UP) c. pp.285-8

    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. Jones (1983) ‘Political Equality and Majority Rule’ in D. Miller and L. Siedentop (eds.) (1983) The Nature of Political Theory (Oxford: Clarendon)

    R. P. Wolff (1976) In Defense of Anarchism (New York: Harper & Row) c. pp.44-6

    The idea is also discussed in some treatments of lotteries:

    N. Duxbury (1999) Random Justice: On Lotteries and Legal Decision-Making (Oxford: Clarendon Press)

    J. Elster (1989) Solomonic Judgements: Studies in the limits of rationality (Cambridge: Cambridge UP)

    B. Goodwin (2005) Justice by Lottery 2nd edition (Exeter: Imprint Academic)

    The idea of lottery voting with n>2 is, I believe, novel - although I briefly suggest such for constitutional amendments (see sec5.5, esp. p.177 of my thesis, available at:

    Ben Saunders

  22. the Democratic party is not a Labor party; it is not a Feminist party; and so on through the range of groups. And this means that no issue has a stable position at the table except for purely extrinsic reasons

    And that's all completely fine with me. After all, the purely extrinsic reasons in this case are themselves fairly stable, reflecting steady popular support for Labor and Feminist positions. I don't see why I should be bothered by this, or why I should particularly care for coalition realpolitik to happen at other levels than the ones it does at present.

    ADHR, by political power I just meant 'the ability to translate your preferences into policy'. The Canadian situation seems to be one in which that power fluctuates with the dynamics of parliamentary coalitions.

  23. Neil,

    Fair enough, although I would say that this is probably a result of your own political interests being in the vicinity of the compromise rather than more closely conformable to most of the interests that have to be compromised to make the compromise possible, and that contribute to the political power of the Democratic party despite being poorly represented by it. No doubt some of the differences on this sort of question will be due to different tastes.


    It occurred to me as a possibility that some of what you are suggesting might still hold if we moved the lottery from the election itself to the pre-election, i.e., if the election were still majoritarian but the slate of candidates was chosen by lottery. This wouldn't preserve the 'every vote makes a different' idea, but it would compensate for it by giving everyone eligible for office an equal chance to be considered for it. This seems to me (prima facie, without having thought the matter through completely) to avoid some of the worries about having the election itself being chancy.

    (I wonder if chancy election might work best in a system where the elected office has a short term and is primarily administrative in nature. These would both minimize worries about dangerous fringe parties.)

  24. I'm attracted to lottery voting, or even just Athenian sortition legislature and giant 'juries'. It makes most sense when you think of it not for executives but legislatures, random sample of 100 or 500 people. If you have lottery voting with districts and your district gets a nutter representative, well, no real loss. And they'll be gone soon anyway; you do things like randomly replace only half at each election but still, you won't reliably get people serving for 20 years.

    OTOH, you get the same benefits of "every vote counts" with proportional representation (as used by most democracies) or direct representation/proxy voting (where instead of reps with equal power, they have power equal to how many votes they got.) PR/DR give more connection between vote and representative, and can keep 'good' or experiences reps around; pure random selection guarantees representation (at least of those who can serve) and not much role for campaigning.

    I'd say try to avoid single powerful executives, vs. strong and representative legislatures. But when you must have them, you want a majority. Runoffs, approval votes, range/score voting, Condorcet, (not instant runoff please, it doesn't seem to do much good; you can safely vote for third parties that don't matter) The US, along with UK and Canada, mostly uses plurality voting. Sigh.

    A variant of lottery voting is pick someone, and let them serve, or choose someone to serve. I've come to think either form is better than the pure random legislature, which eliminates rolls for advertising/campaigning/pressure (arguably good) but disenfranchises those who can't serve when called. E.g. if there are 50 men and 50 women, and 25 of the women are busy raising kids, a non-draft selection will end up 2/3 male, with the 25 mothers having no direct voice. If they get to cast a vote, or pick a replacement when called, then they get a voice.

    GURPS Transhuman Space had what Brandom suggests: random selection of a panel of candidates, who are then given funds to run, and expert/AI help once elected (called "cyberdemocracy", because of the big role of AI help).


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