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. Adit says:

    What about the poor who cannot afford to pay, but nevertheless care about the outcome of the election results, particularly in developing countries, like India?

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    • Jerome Solanum says:

      Easy… make the first vote free.

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      • wiggly says:

        One person one free vote for the poor: one person, limitless votes for the rich. Sure, there’s a solution!

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    • Neil (SM) says:

      They simply sell their votes to more wealthy supporters of their preferential candidate.

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  2. Howard Brazee says:

    Isn’t that what we’re doing now? When Sheldon Aldeson calculates out the cost/benefit ratio of his investments in bribing political campaigns, it is an investment that helps him.

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  3. Sully says:

    I’d like to see the voting curve steeper. 1 vote = $1, 2nd vote = $10, 3rd = $100, 4th = $1000, 5th = $10,000, 6th = $100,000, 7th = $1,000,000 etc… each vote more expensive by a factor of 10.

    However, if this were ever to be implemented, it still wouldn’t change the fact that the rich are going to donate to campaigns more than the poor. It won’t eliminate political advertisements or PACs or Super-PACs. Hence, this will actually ENHANCE the rich’s influence, not equalize it as assumed in the “The first concern…” paragraph.

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    • Dave says:

      It doesn’t matter how steep you make it, the better ‘buy’ is direct purchase of others’ first votes, which is where the money will go.

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      • Tommy Schouw says:

        In “normal” democracies, it’s Illegal to purchase votes. Would the aim still be to keep it illegal, or would that just be seen as a rational extension of the system?

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      • Rob says:

        I agree, Dave. Rather than spend the money on voting your own votes 500 times, a multimillionaire or billionaire would use that money to buy the votes tens of thousands of others. Those others would profit exponentially from selling their vote for more than the dollar it would cost to use it.

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      • Clancy says:

        More important than it being illegal, a secret ballot (which I assume is preserved under this scheme) makes it impractical to buy others’ votes because there’s no proof that they voted the way you paid them to.

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      • Travis says:

        Well, on the other hand it would be much easier under such a system to buy the first, say, 20 votes of 50 people than to buy the first vote of 1000 people. While it may be cheaper to do the latter, it will be more practical to do the former.

        While it increases cost, it will reduce risk of both being caught, as well as the risk of the payees voting for the adverse candidates.

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      • JAM says:

        In reply to Dave,

        This may be true, but by raising the price of subsequent votes, you will also be raising the market value of people’s 1st votes if they choose to sell them. In the end you will still increase the cost to people trying to buy elections.

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      • Andy says:

        It’s actually still possible to buy votes even with a “secret ballot”, depending how it’s implemented. One way is to have people vote absentee (by mail). Another way is to give voters prefilled ballots. Another is to have voters take a photo of their ballot along with some unique identifier (like their ID).

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      • Me says:

        That’s right, Dave. The wealthy buy votes. Levitt says this is a problem….then allows the crickets to go back chirping.

        Good grief. Did Levitt even bother to do the math? For $1.4 billion an election could be completely purchased and delivered.

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    • Eric H says:

      Think of the revenue that would generate! :)

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    • Adam says:

      Interestingly enough, let say we remove the secret vote policy, and allow vote buying. Also, at the same time, make the cost of buying votes scale with the amount of votes you buy, regardless of whose doing the voting. There are some details to work out there, for example who gets the money of the more highly valued votes, but two points. First, I’m not smart enough to game out what that does to the political system, but I think it would be incredibly interesting. Second, that would have the effect of directly distributing money from the incredibly rich to the not so incredibly rich, wouldn’t it?

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  4. Dayna says:

    What about money or volunteer hours or other charitable donation? This system could do a lot of good, both for our federal coffers and understaffed charities. Too bad it’s so anachronistic to the American ideal of democracy that it doesn’t stand a chance of implementation.

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  5. Tommy Schouw says:

    As an european, it’s always interesting to see both how “bad” your voting strategy is, and to see the Stockholm syndrome caused by the widespread corruption.

    Economists are no longer trying to stop the corruption, merely systemize it.

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    • Steve O says:

      I’m very interested to hear about this “widespread corruption” in American voting that you seem to be an expert on.

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  6. Democracy Rules says:

    Like many economic and political science theories, this may sound good on paper, but end up being pure crap in reality.

    Do you think that mine owner who sent his employees the “if Mitt doesn’t win you could all lose your jobs” would hesitate one bit to add $5 to each employee’s pay (or more likely threaten to withhold $5 FROM their pay) to entice force them to vote for Mitt. Or that Sheldon guy who’s given $50 million to Newt and Mitt won’t try to buy the election?

    Just because the current system does not do enough to restrict the wealthy from bastardizing democracy does not mean we should say “screw it” and let them win – even if the theoretical methods create better (but NOT best) results.

    One person, one vote – period.

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    • Travis says:

      It seems to me this would be most problematic in small, rural counties that depend on mining or other energy industries. When the energy co employs a large number of the county population, it would be very easy for them to say to all their employees “If this county votes in Candidate X, everyone gets a $100 bonus.”

      While it would be arguable whether this is “buying” votes or not (because technically they aren’t soliciting directly), it would be even easier to do under the proposed system.

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    • Neil (SM) says:

      I suppose the mine owner believes (or wants his employees to believe) that if his guy doesn’t win then his operating costs — be it from taxes, indirectly through regulations, whatever — will become so great that he will be out of business. In that case, there’s really only so much he can do. If he spends enough on voting to influence the election, the net result is that he may very well be shelling out the same amount of money he would have been had he simply lost the election.

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  7. David Bley says:

    Our system already allows those with more money to exert more influence.

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  8. Seminymous Coward says:

    One huge problem with letting real elections work like that would be the fact that electoral systems are used to decide on the rules for those systems. No amount of television selection bidding will affect the way televisions are selected, but politicians can and do alter the way that they are themselves elected.

    Imagine the following progression: The first new election uses $1 to start with quadratic growth. Later, the rich vote that this changes to the “more fair” system starting at $2. Several more iterations later, the rich have voted that the best system is $1,000 with linear growth fully tax deductible, and the poor have long since stopped having the ability to meaningfully influence results, even in aggregate. Somewhere along the line, restraint in rigging the economic rules to favor the rich would likely have dropped off, too.

    The self-modifying nature of election rules makes their balance precarious. Slippery slope arguments very much apply when there really is an analogue to momentum in the system.

    I’d also note that a system that overtly and explicitly favors the rich is very much at odds with both our inherent sense of fairness and the manufactured consent view of democracy. It’s probably not great for the long-term stability of the country trying it, either.

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    • J. Goard says:

      Seems like long before that point, the relatively poor masses would have realized another factor that influences the type of electoral system we have, namely, the potential to riot, smash department store windows, loot and burn, pull rich people out of their cars and string them up in the square. Whatever incremental change gets made, it has to be rhetorically successful at keeping the vast majority of people complacent, right?

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