An appalling and politically impossible way to improve voting outcomes.

In this post, I propose that elections in large democracies will give better outcomes by changing the voting rules as follows:


For each election, only a random subset of citizens, notified far in advance, can vote. Nothing else is changed.

Why would this help? First, we need to discuss the problem with voting in large democracies.


Why should I spend the effort to become informed before voting? My vote has an extraordinarily low probability of changing the winner of a national election. Suppose that one candidate is much better for the country. Numerically, imagine that candidate A would be $100,000 “better” per citizen. The probability that my vote changes the election is very small. By this estimate, voters in New Mexico in 2004 had approximately a 1 in 10,000,000 chance of their vote determining the election. All other states had much smaller probabilities.

Thus, if I make a large investment of time to carefully evaluate the candidate’s positions, decide who is better for the country, and then vote, I will receive an expected return of $0.01!

Of course the issue with the above is that I am only comparing the costs and benefits to me. If one candidate is really $100,000 better per citizen, the total expected benefit to informing myself should be multiplied by the number of citizens (~300 million). In this case the total expected benefit to figuring out which candidate is better and then voting should be $3 million! (This number is surprisingly high because New Mexicans had the highest chance of influencing the election in 2004.) The problem is that almost none of that $3 million goes the person who put in the work. In economist lingo, educating oneself before voting has large “positive externalities”.

I think the central problem with large democracies is that voters are uninformed. Not because they are stupid or uneducated (1)– because they are rational.

(1) I strongly reject the idea that people are stupid.


The above assumes, of course, that people are strictly selfish beings only seeking to maximize their own utility. Most standard economics is built on this assumption, but in this case, it doesn’t look so good. The rebuttal is:

If the above was true, wouldn’t society descend into anarchy?

I find this rebuttal pretty compelling. Democracy does work fairly well, much better than the above argument would suggest. There are two explanations for this:

  1. Entertainment
  2. Altruism

First, people may choose to learn about candidates simply because they find it fun. Secondly, people simply choose to learn about candidates because they feel a sense of responsibility. They do care about how their vote affects other people, and act accordingly. That is altruism.

Still, I think we can’t dismiss the economist. Why? Ask yourself this:

Suppose you had the only vote. You get the choice, yourself, who should be the next US president. Would you learn more about the candidates than you have bothered to learn now?

I think any honest person would answer, “yes– a great deal more.”


The argument for leaving the decision up to a small number of people is clear. Those people will have a greater stake in the election, so they will take their choices more seriously. Would this really happen? I think so.


If you are not familiar, the US political parties choose their nominees through a staggered process. Different states do not vote simultaneously. Iowa and New Hampshire vote first, and thus wield huge influence on which candidate is chosen. As a result, the people in those states have developed a culture that takes the primaries very seriously.  It is fair to say that the average Iowa primary voter is better informed than the average voter in a state that votes on Super Tuesday.


Of course, is that it is totally unfair that people in two states have so large a choice in who is president! The obvious solution to this would be to move to a simultaneous, national primary. Ignoring the fact that we will take New Hampshire’s primary from their cold, dead hands, would we want this?

Candidates with little money can compete and win in Iowa and New Hampshire through “retail politics”, launching them to a national campaign. With a national primary, it would be even more difficult for a poorly funded candidate to win.

10,000 people

Now, imagine that votes were given to a random subset of the population, say 10,000 people. What would happen?

  • The candidates would personally meet each voter. Those voters would demand and get meetings with the candidates in small groups. The candidates would be forced to actually answer the question asked of them. In a year, to meet each voter, the candidate would need to talk to only 27.39 voters per day.
  • Each voter would both have a personal interest in the election feel a strong sense of personal responsibility for the outcome. With only 10,000 voters, every vote counts. If you have a real chance of changing the winner, you have a real interest in making your choice correctly.
  • The influence of money would be reduced. Initially, I thought it might be reduced almost to zero, but upon reflection this probably wouldn’t happen. The reason is that the voters would be subject to intense lobbying from their friends and neighbors. Thus, candidates might still choose to run TV ads in the hopes of indirect influence on voters.
  • Unfair negative attacks would lose impact, while fair negative attacks would gain impact. Think of how negative attacks work now: Suppose lying candidate A runs an 30 second TV ad falsely accusing honest candidate B of shooting penguins for fun. B then runs a 30 second ad pointing out that this is nonsense. I, the disengaged voter, am left with a cloudy doubt about the truth– perhaps B likes to kill penguins, perhaps not. I am also left more cynical about politics, leading to my further disengagement. Under my proposal, imagine that A makes the same attack. I then meet with B, who personally explains their deep love for the penguin species. B’s staff sends me information on all the pro-penguin legislation B has supported. I am now left only with a distaste for A’s dishonesty.


The biggest problems with this suggestion are:

  1. It is undemocratic.

  2. It will never happen.

“Disenfranchise 99.9% of the population– are you insane?” Well, maybe. However, I believe that the trouble with democracy is that people already feel and are disenfranchised. You are a fool to spend hours and days educating yourself, when your vote will just be a drop in a sea of uninformed votes.

10,000 highly enfranchised voters would do a better job than 200,000,000 distracted.

Most discussion of voting systems focuses on game theoretic issues. Assuming the whole population knows the candidate they want, and voters vote strategically, how can the system be structured to pick the candidate with the highest appeal? There are mathematical results that no voting system exists that satisfy some intuitive criteria, in the case of more than two candidates.

I doubt the importance of this. That model ignores the large cost to a voter of choosing to inform themselves about the candidates. I think instead, voting systems should be designed to give voters an incentive to pay that cost.

Postscript: The ancient Greeks apparently often filled offices through the Sortition method– randomly assign the office to a citizen. My proposal here could be seen as these two steps:

  1. Expanding the electoral college to 10,000 members.

  2. Choosing those member by Sortition.


6 thoughts on “An appalling and politically impossible way to improve voting outcomes.

  1. I like it. Another good way might be to empanel a large grand jury, with subpoena powers, to elect officials.

  2. The extra influence of voters in small states is a feature, not a bug.

    Random over the population isn’t the only reasonable choice. In fact, it’s a pretty horrible one as it increases the bias towards urban centers.

  3. Given there are so few people, what would prevent bribery? One of the voters say they will vote for the candidate whose supporter gives them the most money. It’s hard to bribe enough voters when many millions vote, but with 10000? Seems very possible.

  4. Well, the reason citizens in large democracies are uninformed is because it is irrelevant who wins the election. The two party system dominating large democracies, gives you two parties that are the same. Moreover, they use the same techniques to attract voters; as a result they get just about the same number of votes

    I recall in Greece (small democracy) when 5 or 6 parties were prominent (70’s and 80s) everyone was informed. Now, they also have two parties, almost equivalent. Apparently, many people are uninformed.

    Your proposal is an interesting exercise in the foundations of probability and I would not be surprised if it is implemented in some form in the future. I mean, a group of people chooses one person to vote for them and they pay him/her.
    I wonder how the notion (also ancient greek) of assigning different weights to different votes, within your sample, makes things better or worse.

    Your analysis is first class – you should submit it to the Mathematical Intelligencer.

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