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ParagonProtege comments on Does My Vote Matter? - Less Wrong Discussion
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I'm writing a research paper on electoral reform and - while contemplating Arrow's impossibility theorem - I had the same idea. What's so bad about non-deterministic voting systems that they have to be excluded from the start, especially if (assuming I understand the theorem correctly) they are the only ones that can simultaneously satisfy all of Arrow's other four criteria?
Corruption, or the appearance thereof. Getting everyone to agree that the process actually is random after the outcome is already decided will be nearly impossible.
Have the election determined by a function in which each candidate secretly contributes their own input.
For example:
Each candidate secretly writes down an integer. When everyone is done, they reveal what they wrote. The election is determined by the final two digits of the sum.
As long as even one person is able to keep their input secret, it would be impossible for any candidate to rig the system. Anyone concerned about the election being rigged can unilaterally make harder to rig by working harder to keep their integer a secret.
Better yet: first, an anonymized database of all ballots is made publicly available on the Internet (this can even have IDs that let people check that their vote was recorded correctly). Alice, Bob, and Claire pick integers A, B, C much larger than the number of voters (N), and commit to hashes of those integers (this step can even be done before voting). Then they reveal A, B, and C, compute A+B+C mod N, and use that voter's ballot to determine the outcome of the election.
I like that solution, and so far I can't see any problem with it (as long as at least person randomizes their number, there is no advantage in picking one number over another).
That's an interesting objection, and not one that I had yet thought of. Though, I don't share your pessimism about it being nearly impossible for observers to be certain the process is random. (Or at least as confident that the process is genuine as we are about our current, deterministic voting method.)
On the other hand, I haven't been able to come up with a satisfying solution after thinking about it for the past few minutes. So you could be right. But maybe someone more savvy than I can come up with a better solution.
Right now, few people think that state lotteries are rigged...
There's far less incentive for the government to care about who wins a normal lottery than about who wins an election lottery. (And I've read that in third world countries, the lotteries often are rigged so that cronies of officials win them.)
That's true, so far as I know.
Ironically, there actually is corruption in state lotteries. I remember watching an Dateline NBC documentary about it. Apparently, some stores that sell lottery tickets will buy winning tickets back from their customers at a reduced price and cash in the ticket themselves. (The reason a customer would agree to this is to avoid having to pay back taxes, child support, etc.)
I don't get this. Why would someone who stands to lose out by winning the lottery be buying lottery tickets?
Beyond the cached answer of "people are ridiculously irrational," here are a few reasons why.
In some cases, they may not know that lottery winnings will taken before they buy the ticket. When they go to collect their winnings, an unscrupulous store clerk/manager might then inform them. Or maybe they do know beforehand, but are also aware that they can sell the ticket.
I've also heard of store clerks/managers misleading lottery winners about how difficult it is to collect their winnings. After a certain threshold (to pull a number out of the air, say $1000), winners have to deal with the state directly in order to collect their winnings. I imagine that this is to verify/record the winning ticket and recipient. If the store can convince you that it's more hassle than it's worth, then their offer to buy the ticket off you sounds more enticing.
OK, makes sense.
Good call. See MileyCyrus's solution.
Note that the randomness doesn't need to come into force in all cases. For instance, you could have a Condorcet system using randomness only to determine which method will be used to resolve a cycle.
There's Eliezer's frequent claim, that for every randomized solution, there's a better deterministic solution that possibly requires more thought.
This doesn't necessarily apply. The usual caveat with the anti-randomization advocation is "except when defeating more intelligent or more privileged enemies". These are the same sort of considerations that the voting systems have to handle. (That is, tactical input from motivated individuals in contrived extreme worst case scenarios.)
The core reason that non-deterministic voting systems are excluded in modern politics is that they make it harder to be a career politician and get relected. As politicians are the people who decide how voting systems look like they don't choose non-deterministic voting systems.
In standard discourse one says that political talent can got lost. Good politicians who have no trouble getting relected in the current system suddenly face a real chance of losing their jobs.
For presidential elections, getting a candidate elected president that's hated by 99% of the population seems a bad outcome. A candidate shouldn't only appeal to a small niche of people.