Does one's vote make a difference?

Suppose that there is a simple majority election, with two candidates, and there is a large odd number of voters. Suppose polling data makes the election too close to call. How likely is it that you can decide which candidate wins?

I could look up this stuff, but it’s more fun to figure it out.

A quick and dirty model is this. We have N people other than you voting, each choosing between candidates A and B with probabilities p and 1 − p respectively. You don’t know what p and 1 − p are, but polling data tells you that p is between 1/2 − a and 1/2 + b for some positive numbers a and b. Your vote decides the election provided that exactly N/2 people vote for candidate A. This requires that N be even (if N is odd, at best you can decide between a candidate winning and the election being undecided, so you can’t decide which candidate wins), which has probability 1/2. Given that N = 2n is even, the probability that the other votes are exactly balanced is (a+b)⁻¹ C(2n,n)∫_1/2−a^1/2+bpⁿ(1−p)^n − 1dp, where C(m,n) is the binomial coefficient. Assuming n is large as compared to a and b, the integral can be approximated by replacing its bounds by 0 and 1 respectively, and some work with Mathematica shows that for large n the probability is approximately 1/(N(a+b)).

So what? Well, suppose you think that candidate A will on average make a person in the jurisdiction be u units of flourishing better off than candidate B will, and there are K persons, where K ≥ N + 1 (there are at least as many persons as candidates). So, the expected amount of difference that your voting for A will make is at least Ku/(2N(a+b)). This is at least u/(a+b). Thus, if the polling data gives you a range between 0.48 and 0.52 for the probability of a person’s preferring candidate A, and half of the people in the jurisdiction vote, the expected amount of difference that your vote makes is 25u. This is quite a lot if you think that which candidate wins makes a significant difference u per governed person.

Interestingly, some numerical work with Mathematica also shows that as number of people increases, then the expected amount of difference your vote makes also increases asymptotically, up to the limit of Ku/(2N(a+b)). So for larger jurisdictions, even though the probability of your vote making a difference is smaller, the expected difference from your vote is a bit bigger.

My quick and dirty model is not quite right. Of course, people don’t come to the polls and randomly choose whom to vote for. A more likely source of randomness has to do with who actually makes it to the polls (who gets sick, who has something come up, who decides it’s pointless to vote, etc.). A better model might be this. We have M people eligible to vote, of whom pM want to vote for A and (1−p)M want to vote for B. Some random subset of the M people then votes. My probabilist intuitions say that this is not that different from my model if the number of actual voters is, say, half of the eligible voters. If I had an election that I was eligible to vote in coming, I might try to figure our the more complex model, but I don’t.

Python script for Nanson and Black voting

I made a handy little python script for tabulating group votes with more than two candidates using either Black’s Procedure or Nanson’s Method. Both algorithms are Condorcet compliant. The algorithms require as input a text file with the ballots and control information. Once the algorithm finds a winner (or a bunch of tied winners), it deletes them from the ballots and repeats.

For instance suppose sample.txt contains:

method Black's
require 3
ballot Mickey Donald Sonic
ballot Mickey Sonic Donald
ballot Sonic Mickey Donald

Then:

$ python3 vote.py sample.txt
Options: {'method': "Black's", 'require': 3}
Ballots: 3
Valid ballots: 3
Candidates: ['Donald', 'Mickey', 'Sonic']
Method: Black's
position 1 (Condorcet): Mickey
position 2 (Condorcet): Sonic
position 3: Donald

Black’s Procedure works as follows at each stage: see if there is a Condorcet winner; if not, look for a Borda winner (the first person on each ballot gets a (reversed) Borda score of 0 points; the second gets 1 point; and so on; persons not on a ballot get n points where there are n on the ballot; the winner is determined by the lowest sum of points; note that by default the ballots are modified at subsequent stages by deleting candidates who were already selected, which means the Borda scores change from stage to stage). Nanson’s Method deletes everyone with poorer-than-average Borda score, re-ranks, and repeats until there is a winner or a tie. This is also guaranteed to return a Condorcet winner if there is one.

The code marks winners that were Condorcet winners. That may be helpful to group deliberation as it shows that the decision is bit more robust in that case. (Though a Condorcet winner in kth place, with some non-Condorcet winners before, may not mean much if the earlier winners are dubious.)

The require line specifies how many entries a ballot must contain to be valid (by default, all ballots are valid, even ones with varying numbers of votes; any unranked candidates count as tied after the last ranked candidate). The ballot lines contain the candidates that someone voted for, in order from best to least good. Candidate names are case sensitive and cannot contain spaces. To save typing, one can also introduce abbreviations with the key entry. For instance:

method Black's
require 3
key m Mickey
key d Donald
key s Sonic
ballot m d s
ballot m s d
ballot s m d

Voting and expertise

Here is something that worries me. In a democratic system, voters need to decide questions where not only is the first-order evidence regarding the questions far beyond the area of expertise of the typical voter, but it is far beyond their area of expertise to know who are the reliable experts.

Economic questions seem particularly glaring cases of this. One politician proposes to raise the minimum wage on the grounds that this will improve the earnings of the neediest members of society, and thereby on balance raise up the most vulnerable. Another proposes to keep the minimum wage fixed on the grounds that raising it will lead to greater automation or close some businesses or reduce employment hours, and thereby on balance bring down the most vulnerable. Who is right is largely an empirical question. There is no way to address it without hard data, and the analysisof the data is really difficult.

If I were voting on such an issue (as an expat Canadian, I don’t get to vote either in the US or Canada), I could to talk to colleagues in the Economics Department and try to get their expert opinion. But, frankly, even that probably wouldn’t be very reliable. These issues are ones that economists are going to be divided on, and while I know about the intellectual integrity of my colleagues in the Economics Department, it’s hard to know about their standing in the field and their knowledge of a particular question. And the vast majority of people doesn’t even know any economists personally.

This is really pessimistic. And I don’t see a solution. More education is good, of course, but the level of education that would be needed would be way higher than most people would have either the time or talent for. Maybe the one happy thought is this. When we have controverted empirical questions like that, and we need to make a decision, tossing a coin isn’t a bad way to do it. And voting is no worse than tossing a coin.

Voting for Schmitler

Three people are running for election in Germany: Hitler, Schmitler and Bonhoeffer. Bonhoeffer promises just policies but has no chance of being elected. Hitler promises to kill 50% of minorities. Schmitler promises to kill 80% of minorities. You might think that at this point I will raise the difficult question whether it is permissible, all other things being equal, to vote for Hitler. But I won’t raise exactly that question.

Instead, I want to expand on the above scenario in a different way. Schmitler is incompetent and won’t manage to do more than a quarter of the evils he promises, unlike Hitler who is going to exactly what he promises. So, whom should you vote for? Bonhoeffer who has just policies but won’t be elected? Hitler whose policies are less bad than Schmitler’s, but who will do exactly what he promises? Or Schmitler whose policies are much worse than Hitler’s, but who will do much less bad than Hitler?

There is a good utilitarian case for voting for Schmitler. Here’s an argument for this case. Suppose the elections are occurring in the middle of World War II. It seems that a very reasonable thing for Allied spies to do is to ensure that incompetent people run Nazi Germany. One means to that goal is stuffing ballot boxes with votes for Schmitler. And while typically one shouldn’t stuff ballot boxes, this seems to be a case where the stuffing of ballot boxes would be permissible. So, Allied spies, we suppose, are stuffing ballot boxes in favor of Schmitler. Helga is a German resister to Nazism, working for the Allies. She is an excellent prestidigitator and is going to the voting booth with a sleeve full of Schmitler ballots, in order to stuff the box surreptitiously. If the Allied spies are doing the right thing, Helga is doing the right thing.

Now, if Helga can permissibly stuff the ballot box in favor of Schmitler, then she could permissibly do this: put in a vote for Bonhoeffer (or Hitler), then surreptitiously remove that ballot and replace it with a fake ballot in favor of Schmitler. But if that’s permissible for her, then it would be very strange if she wasn’t permitted simply to vote for Schmitler.

So, it seems, it is permissible to vote for Schmitler on the grounds that he is incompetent, despite the fact that his policies are significantly worse than Hitler’s. But if this is permissible, then it would be a fortiori permissible to vote for Schmitler if he promised to kill 5% of minorities, and this would seem to be permissible even if Schmitler were as competent as Hitler. So, we have an argument that it is permissible to vote for a candidate whose policies represent a lesser evil. Of course, one should never endorse an evil, even a lesser one. So, it follows that voting for a candidate is not endorsement of the candidate’s policies.

I am not wholly convinced by the above argument. I feel a certain pull to the strange view that while it would be permissible for Helga to replace her real Bonhoeffer vote with a Schmitler fake ballot, it would not be permissible for her to vote for Schmitler. After all, strange circumstances make for strange conclusions.

A reason why voting methods are compromises

Voting involves compromise on two levels. On the ground level, a vote involves coming to a compromise decision. But on the meta level, a voting system embodies compromise between different desiderata. Arrow's Theorem is a famous way of seeing the latter point. But there is also another way of seeing it, which in one way goes beyond Arrow's Theorem: while Arrow's Theorem only applies where there are three or more options, what I say applies even in binary cases.

We suffer from both epistemic and moral limitations. Good voting systems are a way of overcoming these, by combining the information offered by us in such a way that no small group of individuals, suffering as it may from epistemic or moral shortcomings, has too much of a say. It is interesting to see that there is an inherent tension between overcoming epistemic and moral limitations.

Consider one of two models. On both models, a collection of options is offered to a population.

1. Model 1: Each voter comes up with her honest best estimate of the total utility of each option, and offers a report of her estimate.
2. Model 2: Each voter comes up with her honest best estimate of the utility for her of each option, and offers a report of her estimate.

On the assumption that (a) the voters' errors in their estimations are independent Gaussians with mean zero and we have no information as to who has bigger variances, and that we want to maximize total expected utility (which will be approximately true) and (b) the voters accurately report their estimates, there is provably an optimal voting system under both models: we simply arithmetically average the voters' estimates and select the option with the highest average utility estimate (see my earlier post on this for some computer simulation data). Any voting system whose departs from this will be inoptimal under these circumstances.

Assuming that whatever people are going to say in a vote is going to be somehow based on their estimates of utility on the whole or utility to them, this averaging system is the best way to leverage the information scattered in the population. Unfortunately, while this is a good way to overcome our epistemic limitations, it does terribly with regard to our moral limitations. If one lies boldly enough, namely comes up with utility estimates that are far more inflated than anybody else's, one controls the outcome of the vote. Let's say that option 2 is the best one for me. Then I simply specify that the utility for option 2 is 10^100000000 and for option 1 is −10^100000000. And of course, there will be an arms race in the population to specify big numbers if there is more than one dishonest member of the population. But in any case, the dishonest will win.

In other words, the optimal system in the case of honest utility estimates is pretty much the worst system where honesty does not generally hold. A good voting system for morally imperfect voters must cap the effect each voter has. But in capping the effect each voter has, information can will in general be lost.

This is most clear in Model 2. We can imagine that an option moderately benefits a significant majority but horrendously harms a minority. Given honest utility reports from everyone and the averaging system, the option is likely to be defeated, since the members of the minority will report enormously negative utilities that will overcome the moderate positive utilities reported by members of the majority. But as soon as one caps the effects of each voter, the information about the enormously negative utilities to the minority will be lost. Model 1 is more helpful (presumably, civic education is how we might get most people to vote according to Model 1), but information will still be lost due to the differences in epistemic access to the total utility. On Model 1, capping will lose us the case where one individual genuinely has information about an enormous negative effect but is unable to convince others of this information. But capping of some sort is necessary because of moral imperfection.

(The optimal method of utility estimation also faces the problem that we are better at rank orderings than at absolute utilities. This can in principle be overcome to some degree by giving people additional hypothetical options to rank-order and then recovering utility estimates from these.)

A brief way to make the point is this. The more trusting a voting system is, the more information it brings to the table; but the more trusting a voting system is, the worse it does with regard to moral imperfection. A compromise is needed in this regard. And not just in voting.

Beating Condorcet (well, sort of)

This builds on, but also goes back over the ground of, my previous post.

I've been playing with voting methods, or as I might prefer to call them "utility estimate aggregation methods." My basic model is there are n options (say, candidates) to choose between and m evaluators ("voters"). The evaluators would like to choose the option that has the highest utility. Unfortunately, the actual utilities of the options are not known, and all we have are estimates of the utilities by all the evaluators.

A standard method for this is the Condorcet method. An option is a Condorcet winner provided that it "beats" every other option, when an option x "beats" an option y provided that a majority of the evaluators estimates x more highly than y. If there is no Condorcet winner, there are further resolution methods, but I will only be looking at cases where there is a Condorcet winner.

My first method is

• Method A: Estimate each option's utility with the arithmetical average of the reported utilities assigned to it by all the evaluators, and choose the option with the highest utility.

(I will be ignoring tie-resolution in this post, because all the utilities I will work with are real-numbered, and the probability of a tie will be zero.) This method can be proved to maximize epistemically expected utility under the

• Basic Setup: Each evaluator's reported estimate of each option's utility is equal to the actual utility plus an error term. The error terms are (a) independent of the actual utilities and (b) normally distributed with mean zero. Moreover, (c) our information as to the variances of the error terms is symmetric between the evaluators, but need not be symmetric between the options (thus, we may know that option 3 has a higher variance in its error terms than option 7; we may also know that some evaluators have a greater variance in their error terms; but we do not know which evaluators have a greater variance than which).

Unfortunately, it is really hard to estimate absolute utility numbers. It is a lot easier to rank order utilities. And that's all Condorcet needs. So in that way at least, Condorcet is superior to Method A. To fix this, modify the Basic Setup to:

• Modified Setup: Just like the Basic Setup, except that what is reported by each evaluator is not the actual utility plus error term, but the rank order of the actual utility plus error term.

In particular, we still assume that beneath the surface—perhaps implicitly—there is a utility estimate subject to the same conditions. Our method now is

• Method B: Replace each evaluator's rank ordering with roughly estimated Z-scores by using the following algorithm: a rank of k (between 1 and n) is transformed to f((n+1/2−k)/n), where f is the inverse of the cumulative normal distribution function. Each option's utility is then estimated as the arithmetical average of the roughly estimated Z-scores across the evaluators, and the option with the highest estimate utility is chosen.

Now time for some experiments. Add to the Basic Setup the assumptions that (d) the actual utilities in the option pool are normally distributed with mean zero and variances one, and (e) the variances of all the evaluators' error terms are equal to 1/4 (i.e., standard deviation 1/2). All the experiments use 2000 runs. Because I developed this when thinking about grad admissions, the cases that interest me most are ones with a small number of evaluators and a large number of options, which is the opposite of how political cases work (though unlike in admissions, I am simplifying by looking for just the best option). Moreover, it doesn't really matter whether we choose the optimal option. What matters is how close the actual utility of the chosen option is to the actual utility of the optimal option. The difference in these utilities will be called the "error". If the error is small enough, there is no practically significant difference. Given the normal distribution of option utilities, about 95% of actual utilities are between -2 and 2, so if we have about 20 option, we can expect the best option to have a utility of somewhere of the order of magnitude of 2. Choosing at random would then give us an average error of the order of magnitude of 2. The tables below give the average errors for the 2000 runs of the experiments. Moreover, so as to avoid between different choices of resolution methods, I am discarding data from runs during which there was no Condorcet winners, and hence comparing Method A and Method B to Condorcet at its best (interestingly, Method A and Method B also work less well when there was no Condorcet winner). Discarded runs were approximately 2% of runs. Source code is available on request.

Experiment 1: 3 evaluators, 50 options.

Condorcet	0.030
Method A	0.023
Method B	0.029

So, with a small number of evaluators and a large number of options, Method A significantly beats Condorcet. Method B slightly beats Condorcet.

Experiment 2: 50 evaluators, 50 options.

Condorcet	0.0017
Method A	0.0011
Method B	0.0015

So we have a similar distribution of values, but of course with a larger number of evaluators, the error is smaller. It is interesting, however, that even with only three evaluators, the error was already pretty small, about 0.03 sigma for all the methods.

Experiment 3: 3 evaluators, 3 options.

Condorcet	0.010
Method A	0.007
Method B	0.029

Method B is much worse than Condorcet and Method A in this case. That's because with three options, the naive Z-score estimation method in Method B fails miserably. With 3 options Method B is equivalent to a very simple method we might call Method C where we simply average the rank order numbers of the options across the evaluators. At least with 3 options, that is a bad way to go. Condorcet is much better, and Method A is even better if it is workable.

Experiment 4: 50 evaluators, 3 options.

Condorcet	0.0003
Method A	0.0002
Method B	0.0159

The badness of Method B for a small number of options really comes across here. Condorcet and Method A really benefit from boosting the number of evaluators, but with only 3 options, Method B works miserably.

So, one of the interesting consequences is that Method B is strongly outperformed by Condorcet when the number of options is small. How small? A bunch of experiments suggests that it's kind of complicated. For three evaluators, Method B catches up with Condorcet at around 12 options. Somewhat surprisingly, for a greater number of evaluators, it needs more options for Method B to catch up with Condorcet. I conjecture that Method B works better than Condorcet when the number of options is significantly greater than the number of evaluators. In particular, in political cases where the opposite inequality holds, Condorcet far outperforms Method B.

One could improve on Method B, whose Achilles heel is the Z-score estimation, by having the evaluators include in their rankings options that are not presently available. One way to do that would be to increase the size of the option pool by including fake options. (In the case of graduate admissions, one could include a body of fake applications generated by a service.) Another way would be by including options from past evaluations (e.g., applicants from previous years). Then these would enter into the Z-score estimation, thereby improving Method B significantly. Of course, the down side of that is that it would be a lot more work for the evaluators, thereby making this unworkable.

Method A is subject to extreme evaluator manipulation, i.e., "strategic voting". Any evaluator can produce any result she desires by just reporting her utilities to swamp the utilities set by others. (The Basic Setup's description of the errors rules this out.) Method B is subject to more moderate evaluator manipulation. Condorcet, I am told, does fairly well. If anything like Method A is used, what is absolutely required is a community of justified mutual trust and reasonableness. Such mutual trust does, however, make possible noticeably better joint choices, which is an interesting result of the above.

So, yes, in situations of great trust where all evaluators can accurately report their utility estimates, we can beat Condorcet by adopting Method A. But that's a rare circumstance. In situations of moderate trust and where the number of candidates exceeds the number of evaluators, Method B might be satisfactory, but its benefits over Condorcet are small.

One interesting method that I haven't explored numerically would be this:

• Method D: Have each evaluator assign a numerical evaluations to the options on a fixed scale (say, integers from 1 to 50). Adjust the numerical evaluations to Z-scores, using data from the evaluator's present and past evaluations using some good statistical method. Average these estimated Z-scores across evaluators and choose the option with the highest average.

Under appropriate conditions, this method should converge to Method A over time in the Modified Setup. There would be possibilities for manipulation, but they would require planning ahead, beyond the particular evaluation (e.g., one could keep all one's evaluations in a small subset of the scale, and then when one really wants to make a difference, one jumps outside of that small subset).

An optimal voting method (under some generally implausible assumptions)

Let me qualify what I'm going to say by saying that I know next to nothing about the voting literature.

It's time for admissions committees to deliberate. But Arrow's Theorem says that there is no really good voting method with more than two options.

In some cases, however, there is a simple voting method that, with appropriate assumptions, is provably optimal. The method is simply to have each voter estimate a voter-independent utility of every option, and then to average these estimates, and choose the option with the highest average. By a "voter-independent utility", I mean a utility that does not vary from voter to voter. This could be a global utility of the option or it could be a utility-for-the-community of the voter or even a degree to which a certain set of shared goals are furthered. In other words, it doesn't have to be a full agent-neutral utility, but it needs to be the case that the voters are all estimating the same value—so it can depend on the group of voters as a whole.

Now if we are instead to choose n non-interacting options (i.e., the utilities of the options are additive), then we just choose the n with the highest averages. Under some assumptions, these simple methods are optimal. The assumptions are onerous, however.

Voting theory, as far as I can tell, is usually conducted in terms of preferences between options. In political elections, many people's preferences are probably agent-centered: people are apt to vote for candidates they think will do more for them and for those they take to be close to them. In situations like that, the simple method won't work, because people aren't estimating voter-indepenent utilities but agent-centered utilities.

But there are cases where people really are doing something more like estimating voter-independent utilities. For instance, take graduate admissions or hiring. The voters there really are trying to optimize something like "the objective value of choosing this candidate or these candidates", though of course their deliberations suffer from all sorts of errors.

In such cases, instead of thinking of the problem as a preference reconciliation problem, we can think of it as an estimation problem. We have a set of unknown quantities, the values of the options. If we knew what these quantities are, we'd know what decision to take: we'd go for the option(s) with the highest values. Instead, we have a number of evaluators who are each trying to estimate this unknown. Assume that each evaluator's estimate of the unknown quantity simply adds an independent random error to the quantity, and that the error is normally distributed with mean zero. Assume, further, that either the variances of the normal errors are the same between evaluators or that our information about these variances is symmetric between the evaluators (thus, we may know that evaluators are not equally accurate, but we don't know which ones are the ones who are more accurate). Suppose that I have no further relevant information about the differences in the values of the options besides the evaluators' estimates, and so I have the same prior probability distribution for the value of each option (maybe it's a pessimistic one that says that the option is probably bad).

Given all of the above information, I now want to choose the option that maximizes, with respect to my epistemic probabilities, the expected value of the option. It turns out by Bayes' Theorem together with some properties of normal random variables that the expected value of an option o, given the above information, can be written Aa₀+Ba(o), where a₀ is the mean-value of my baseline estimate for all the options and a(o) is the average of the evaluators' evaluations of o, and where both A and B are positive. It follows that under the above assumptions, if I am trying to maximize expected value, choosing the option(s) with the highest value of a(o) is provably optimal.

Now there are some serious problems here, besides the looming problem that the whole business of numerical utilities may be bankrupt (which I think in some cases isn't so big an issue, because numerical utilities can be a useful approximation in some cases). One of them is that one evaluator can skew the evaluations by assigning such enormous utilities to the candidates that her evaluations swamp everyone else's data. The possibility of such an evaluator violates my assumption that each person's evaluation is equal to the unknown plus an error term centered on zero. Such an evaluator is either really stupid, or dishonest (i.e., not reporting her actual estimates of utilities). This problem by itself is enough to ensure that the method can't be used except in a community of justified mutual trust.

A second serious problem is that we're not very good at making absolute utility judgments, and are probably better at rank ordering. The optimality condition requires that we work with utilities rather than rank orderings. But in a case where the number of options is largish—admissions and hiring cases are like that—if we assume that value is normally distributed in the option pool, we can get an approximation to the utilities from an evaluator's rank ordering of the n options. One way to do this is to use the rank ordering to assign estimated percentile ranks to each option, and then convert them to one's best estimate of the normally distributed value (maybe this can just be done by applying the inverse normal cumulative distribution function—I am not a statistician). Then average these between evaluators. Doing this also compensates for any affine shift, such as that due to the exaggerating evaluator in the preceding paragraph. I can't prove the optimality of this method, and it is still subject to manipulation by a dishonest evaluator (say, one who engages in strategic voting rather than reporting her real views).

I think the above can also work under some restrictive assumptions even if the evaluators are evaluating value-for-them rather than voter-independent value.

The basic thought in the above is that in some cases instead of approaching a voting situation as a preference situation, we approach it as a scientific estimation situation.

Voting and conflict of interest

Isn't it odd that the usual conflict of interest restrictions on corporate decision-making don't apply in voting situations? If we were hiring, and a candidate was a close relative of mine, I would be expected to recuse myself. However not only is it considered acceptable to vote in elections for a close relative, but even for oneself. Moreover, voters whose stand to benefit from a particular candidate's being elected—e.g., because that candidate promises a tax break to some class of which they are a member—are not expected to recuse themselves from the election.

I think some of these things can be justified. In hiring, the primary question isn't which candidate's hire would most benefit the individual members of the organization. Rather, the question is which which candidate would best further the mission of the organization. When significant private interests that are not aligned with the interests of the organization come into play, one's decision-making runs the danger of becoming skewed, and one may well need to recuse oneself. But it is not always necessary to recuse oneself when one has significant private interests when these interests are aligned with the goals of the organization. Thus, if I think a candidate would make a good research partner for me, and hence I have a significant interest in the candidate's being hired, this interest typically need not force a recusal (though one can imagine circumstances when it would). Now, in voting, one is making decisions for the good of the polis. But the good of the polis includes many of one's own goods. Therefore, many of one's own interests are automatically aligned in the interest of the community. It is in my interest to eat in order to preserve my life, and if I am a member of the community, then the preservation of my life is included in one of the primary goals of the community—the preservation of the lives of the members. However, if it is obvious to one that one's own interest conflicts with the on-balance interest of the community, recusal might still be appropriate, as far as this argument goes.

It may even be justifiable to vote for oneself. For, maybe, one isn't really voting for oneself, but for one's policies. And these policies one has, presumably, thought carefully through, and one did not adopt these policies because they were one's own, but because they seemed right. But this does not, I think, justify voting for close relatives other than oneself. For there, there is apt to be a bias which, paradoxically, may not be present in one's own case. While it at least borders on incoherence to adopt a position because it is one's own, it is easy and coherent (and sometimes rational) to adopt a position because it is that of someone close to us.

Elections question

Stalin and Mother Teresa are running for Prime Minister of Canada. Stalin has a well-publicized plan to murder all the Ukrainians, of whom there are a million. Moreover, his economic policies are stupid, resulting in the impoverishment of the middle class, and no improvement for the needy. Mother Teresa is not only virtuous, but also extremely well-informed about economics, and has policies that promise great economic improvement for the needy, and no loss for the rich. So far, the choice seems easy. The night before the elections, an omniscient and perfectly truthful being tells you—and you know that this is true—that if Stalin is elected, he will succeed in all his plans—a million Ukrainians will be murdered, and the economy will be destroyed. But the being also tells you that if Mother Teresa is elected, earthquakes will destroy Toronto and Montreal, directly killing two million people, and despite Mother Teresa doing the best that can be done, the country will be plunged into an economic depression, whose net effect is the same as that of Stalin's economic policies. If Stalin is elected, the earthquake will happen in an uninhabited area (maybe the military parades will redistribute the geological stress). Oh, and neither Mother Teresa, nor Stalin, nor anybody other than you knows about the earthquake issue--and nobody will believe you if tell them.

The results of electing Stalin are, thus, better than of electing Mother Teresa: a million die, while on Mother Teresa's watch, two million die. Whom should you vote for?

I am not claiming that this has any significant resemblance to the upcoming Canadian or U.S. or other elections.

[Edited: Added lack of others' knowledge of earthquake condition. Also, fixed a typo.]