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!


Ok, I see two potential improvements:
1. Since it’s important to have as few barriers to voting as possible, make the first vote free, and apply the cost structure to any additional votes.
2. The reason this system favors the rich, is that the rich have a declining marginal value of their money. So the system is not measuring the strength of your political preference, but the ratio of your political preference to the marginal value of your dollar, which for a very rich person might be high, even if his political preference were weak.
Index the cost of additional votes to the person’s income (from that year income tax returns) say 0.01% of gross adjusted income.

So the formula becomes: C=I*(0.0001)*(n-1)^2

Sure the system would be a huge pain to implement, but as long as were wishing, I’d like a pony.

Seminymous Coward

This is hugely better, but it's still problematic for two reasons. First, the marginal utility of money is not directly proportional to its percentage of income, although it's substantially closer than dollar amounts. Second, the tax-related definition of the word "income" is warped to the point of inaccuracy, particularly for the wealthy.


Not to mention the fact that we would hear all sorts of noise about "class warfare" and other practical political problems and other incentives it may create.

Under a system such as this one, A Wal-Mart employee may only cost a few hundred dollars for 10 or 20 votes. While say, the owner would be paying thousands of dollars for his second vote.

Under such a situation, there is a huge disincentive for the owner to take part in the process in the intended (and legal) manner. So then if the owner really cares about the election, it would make more sense for him to set up some other method to secure votes, such as paying his employees (or giving bonuses depending on the outcome, or threatening firing as we've seen in this election).

Further, you might argue that what makes this an even more perverse incentive is that it would give the owner a strong incentive to artificially depress the wages on his employees, to ensure that it remains cheap to buy their vote. Then, he can use the money saved to sweeten the deal further with each employee.

Seems like there would have to be iron clad checks against such behavior in such a system, and I am not confident that such checks could be instituted.



It WOULD be a nice way to gather taxes... With the added incentive that the rich would actually volunteer to pay more...


My esteem for the U/Chicago has dipped to a new low with your vote for plutocracy.

Ridiculous to discuss such a thing as the courts would never approve it, and certainly it
would never get through Congress or passed by the states.

Most people aren't rich, why should they forfeit anything they have.

Democrats would hate this and they control in prez elections: CA, NY, IL, NJ, CT, PA,

How would the Founders feel about plutocracy or theocracy, another semi-popular idea
tho express a bit more quietly?

Even scalia says, if it's not in original Constitution, and PLUTOCRACY IS NOT, he ain't going
for it. Can you imagine narrow minded scalia voting with the Dems on SCOTUS. You could get
roberts with the Dems again too, likely kennedy. Who knows about alito and brain dead thomas,
never speaks, not sure what else he does.

Eric M. Jones.

"...So restricting campaign spending, in conjunction with this voting scheme, might be more democratic than our current system...".

...when pigs have wings and Hell freezes over....

I would like to see long prison sentences for major vote fraud. I mean Diebold (lawsuits and investigations still pending), whose voting machine division was acquired by Election Systems and Software (ES&S).


I find it troubling that you would state

" In our existing system of campaign contributions, there can be little doubt that the rich already have far more influence than the poor. "

in this article when previousely (and consistently) you've argued for the non-influence of campaign contributions in outcomes...

I'm not saying one denies the other, but it sure looks quite disrupting... As for the rest, sincere admiration from an anonymous economist


I like this idea and even went to the trouble of RTFS. I think a change that would make it slightly more palatable to the US populace is to shift the signs on the first vote. Instead of "paying" $1 to vote once, you "get" $1 to vote once. Then every vote after that is exponentially price.

- This incentivises all people to vote (even economists), thus [probably] balancing the 500 votes one person might buy with 500 people voting once.
- The cost is paid for by people who vote more than once (3:1), so it's cost free.
- It somewhat mitigates "vote buying" in that the buyer has to cover the second vote price (plus the voter's cut) which is much higher than buying one vote.


Isn't this already being tested on InTrade ( where you can bet on the election?


It's instantly obvious that it's much cheaper for the rich to donate to their fellow partisans in order to buy votes. So it's pretty much guaranteed that this system would fail.

If you want votes to capture the strength of preferences, then just use range voting. Arrow's Impossibility Theorem and the related theorems simply don't apply to it because it's cardinal rather than ordinal.


Donate all the money raised to the people who voted for the losing candidate. That way everybody's happy.

Charles L.

I don't like squaring. I'm tempted to say X^10, but after 3 votes most people would just give up. Another idea would be to try X^2 for the first say 4 or 5 votes, and every consecutive vote costs 10 times as much, so as to dissuade excessive vote-buying. Alternatively, you could have every additional vote be weighed less and cost more. The second vote costs $4, but only buys you half a vote, the third vote costs $8, but only buys you a quarter. This way we can say that no one individual has even twice the democratic say of his fellow man.

David Leppik

Others have mentioned numerous faults with this system. I'll mention only one.

Explicitly tying money to votes turns voting from a purely civic activity to a monetary activity. As with many things,* once you bring money into the equation, it changes how people view it.

(*A colorful example mentioned in the Freakonomics book is sex.)


The other snag with this scheme is that it basically introduces a poll tax, which have been declared illegal pretty much everywhere on the basis of disenfranchising voters who cannot afford the fee/tax.


I'd turn the payment on its head: your vote counts proportional to the square root of the amount of taxes you paid in the previous 4 years. People who put the most money in in taxes should be entitled to the largest consideration in the election process. People paying less than $1 in taxes would get a default value of 1. I think this system would create a feedback loop that would drastically reduce tax rates; a default, followed by greatly reduced government services, would follow. Perhaps the resulting new policies would be seen as more "fair."

While I'm serious about the above suggestion, here is one that I don't think is a good idea... if you want to increase voter participation and allow people to feel that their vote "counts" then each vote is written on a raffle ticket, a ticket is drawn on November 6th, and that luck winner's vote determines the outcome. For the voter's safety, the owner of the winning ticket would not be disclosed.