An Alternative to Democracy?

(Photo: Kim)

With the U.S. presidential election nearly here, everyone seems to have politics on their mind.  Unlike most people, economists tend to have an indifference towards voting.  The way economists see it, the chances of an individual’s vote influencing an election outcome is vanishingly small, so unless it is fun to vote, it doesn’t make much sense to do so.  On top of that, there are a number of theoretical results, most famously Arrow’s Impossibility Theorem, which highlight how difficult it is to design political systems/voting mechanisms that reliably aggregate the preferences of the electorate.

Mostly, these theoretical explorations into the virtues and vices of democracy leave me yawning.

Last spring, however, my colleague Glen Weyl mentioned an idea along these lines that was so simple and elegant that I was amazed no one had ever thought of it before.  In Glen’s voting mechanism, every voter can vote as many times as he or she likes.  The catch, however, is that you have to pay each time you vote, and the amount you have to pay is a function of the square of the number of votes you cast.  As a consequence, each extra vote you cast costs more than the previous vote.  Just for the sake of argument, let’s say the first vote costs you $1.  Then to vote a second time would cost $4.  The third vote would be $9, the fourth $16, and so on. One hundred votes would cost you $10,000.  So eventually, no matter how much you like a candidate, you choose to vote a finite number of times.

What is so special about this voting scheme?  People end up voting in proportion to how much they care about the election outcome.  The system captures not just which candidate you prefer, but how strong your preferences are.  Given Glen’s assumptions, this turns out to be Pareto efficient — i.e., no person in society can be made better off without making someone else worse off.

The first criticism you’ll likely make against this sort of scheme is that it favors the rich.  At one level that is true relative to our current system.  It might not be a popular argument, but one thing an economist might say is that the rich consume more of everything – why shouldn’t they consume more political influence? In our existing system of campaign contributions, there can be little doubt that the rich already have far more influence than the poor.  So restricting campaign spending, in conjunction with this voting scheme, might be more democratic than our current system.

Another possible criticism of Glen’s idea is that it leads to very strong incentives for cheating through vote buying.  It is much cheaper to buy the first votes of a lot of uninterested citizens than it is to pay the price for my 100th vote.  Once we put dollar values on votes, it is more likely that people will view votes through the lens of a financial transaction and be willing to buy and sell them.

Given we’ve been doing “one person, one vote” for so long, I think it is highly unlikely that we will ever see Glen’s idea put into practice in major political elections.  Two other economists, Jacob Goeree and Jingjing Zhang have been exploring a similar idea to Glen’s and testing it in a laboratory environment. Not only does it work well, but when given a choice between standard voting and this bid system, the participants usually choose the bid system.    

This voting scheme can work in any situation where there are multiple people trying to choose between two alternatives — e.g., a group of people trying to decide which movie or restaurant to go to, housemates trying to decide which of two TV’s to buy, etc.  In settings like those, the pool of money that is collected from people voting would be divided equally and then redistributed to the participants.

My hope is that a few of you might be inspired to give this sort of voting scheme a try.  If you do, I definitely want to hear about how it works out!

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  1. chris9059 says:

    “What is so special about this voting scheme? People end up voting in proportion to how much they care about the election outcome.”

    This statement is simply false. Like a great many arguments made by economists it ignores the fact that wealth has declining marginal utility. David Koch could spend $10 million on votes without sacrificing the fulfillment of any other desires (indeed it is reported the Kochs have spent $50 million in this election) that does not mean he “cares” more about the outcome of an election then someone who can only afford to spend $10 on votes.

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  2. crash_dt says:

    If done right on a national scale one could imagine a small economy of vote trades, like on eBay :-) … guess it’d have to be a lot more secure and vote proving would be difficult. ie. There’s no way to know that the person whose vote I bought on the other side of the country will cast it in the manor which we agreed, even a computerized system to track this or ‘lock’ votes in at time of sale wouldn’t be trusted nationally, and would be prone to hacking as any system is no matter it’s encryption.
    That mess aside … sounds very economical. But I suppose you’d have to set a minimum sell price that is quite high, then it may have an effect to help almost stimulate the economy directly from the rich to the poor. Then I suppose “vote crime” would spring up … hmm interesting system in small groups for an outcome that is not so potentially or perceptually life affecting.
    heh … that was wordy, my apologies … just got me thinking as Freakonomics always does!

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  3. Todd Sullivan says:

    There seems to be an overwhelming assumption that folks will sell their votes to folks who want them to vote inconsistently with their own views. If the Republicans and Democrats are similarly funded, can’t you sell your vote to the candidate you want to elect? And wouldn’t that be the optimal solution? If voting 10 times costs a total of $375, aren’t you going to be willing to sell those 10 votes to the candidate you support for $375 (i.e., without profit), while voting against your personal interest would require a premium.

    And I’m not sure how this system creates an opportunity to buy other people’s votes that did not exist already. This system only creates an opportunity for volume purchasing.

    I don’t think deviating from one vote per person could ever get popular support, but I think it would be a nice government revenue source and it could funnel money away from the other irritating campaign expenditures. And I don’t think a secret ballot minimizes corruption, I think it merely changes its form. If you have in excess of a million dollars passing hands within each voting station, well I don’t think you can have money, politics, and not have corruption.

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  4. Richard says:

    There’s a good theoretical reason why this isn’t a good idea. What Steve suggests is a Bayesian prior: the strength of conviction should also be weighed in the vote-as-assessment. But what if, as in a neural network, an equally-weighted distribution is better, since you don’t necessarily believe that strength of conviction necessarily achieves a better outcome?

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  5. Clifton says:

    If your goal is to let people who care more vote more, why not scale the price by net worth? Say, first vote free, and then nth vote costing .01% of net worth times n^2. That way everyone can have between 1 and 100 votes. This would save Levitt’s voting scheme from being based on obviously false assumptions about the marginal utility of wealth.

    One could also allow for other ways of showing that one cares. Perhaps one’s vote could count as the square root of the number of minutes you’re willing to spend waiting. (Suddenly Republican election officials would discover that they actually could do something about wait times in Broward county.)

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  6. Richard Townsend says:

    I think 1oo votes would be more costly than $10,000.00 as that is only the cost of the one hundredth vote. Would you not have to add up the costs of the previous 99 votes to the tally? 1, 4, 9, 16……..the 99th vote would cost $9801.00. I’m sure someone can do the math.

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  7. Jeroen says:

    The obvious problem seems to be that this assumes that dollar value and preference are somehow linked. Surely, this would only be the case if you priced the votes according to peopl’s income.

    The 10th vote costs a poor person relatively more (v-a-v his income) than the 100th vote of a rich person.

    So why is dollar value used instead of percentage of income?

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  8. Jaime Hammond says:

    Why not instead of being able to buy votes with money, you buy them with time? Like, say, you get an extra vote for every 4 hours spent doing some sort of volunteer work. While the amount of available leisure time to convert to votes might not be evenly distributed, it’s certainly much more so — after all, nobody could possibly have more than 24 times as much as anyone else. What’s more, how much work you’re willing to do is a much better indicator of how much you care about something than how much you’re willing to spend.

    Of course, we actually have this kind of system somewhat in place already: if this election cycle has shown us anything, it’s that the returns from a strong ground game — more volunteers making phone-calls, knocking on doors, getting out the vote — diminish a heck of a lot slower than those from as spending.

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