Double Blind Voting
Submitted by Fletcher, who has posted here previously. Welcome back!
The economic and mathematical analysis of voting has generated a large amount of literature. Ever since Ken Arrow showed that there is no social choice function that satisfies the logical choice properties, people have sought to find the next best solution. Recently, Marginal Revolution had a thread about range voting that generated a lot of discussion about voting systems in general. I won’t bore you with the details of range voting, but to say that you assign a score to multiple options within a range of numbers. The highest score then wins the election. This is actually similar to a Borda Count, where the range in equivalent to the number of options.
However, voters in the booth still have the problem of mapping a multidimensional preference set to a single candidate. Thus, I propose a double blind voting system. This system does not require the voter to map preferences to a candidate. In fact, the candidates will be unknown. The voter participates in a survey in which the voter declares preferences across many issues in society. And then, with each issue, the voter will rank the issue in terms of importance.
Potential candidates for whichever office is open privately declare candidacy for an open office. They too must submit a declaration/survey form but they do not rank the issues in terms of relative importance; they only declare their preference.
For example, suppose there are only three issues affecting a society: Guns, healthcare, and military intervention abroad. Then, on a sliding scale of 1-10, people in the survey will declare their preference for government involvement on these issues.
Suppose that these are the results of the voting declarations, where the composite ranking is a value that shows which issue is the most important to the greatest percentage of voters:
| Gov’t Level | Low | Med | High | Composite Rank |
|||||||
|---|---|---|---|---|---|---|---|---|---|---|---|
| Issue | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | |
| Guns | 10% | 15% | 20% | 20% | 5% | 0% | 0% | 0% | 15% | 15% | 45% |
| Health Care | 2% | 5% | 3% | 10% | 12% | 20% | 28% | 10% | 7% | 3% | 40% |
| Military | 1% | 0% | 3% | 10% | 50% | 30% | 0% | 3% | 3% | 0% | 15% |
Since we have the public’s preferences independent of the candidate running, we can now map a candidate’s declarations with the public’s preferences. Mathematically, I was thinking something along the lines as a sum-of-squared-difference-with-the-mode calculation. Suppose candidate X declares a 3 on Guns, a 4 on Healthcare, and a 5 on Military. Then candidate X would receive a (assuming that the mode on Guns is 3.5) .25 score for Guns, a 9 score for Healthcare, and a 0 score for Military. Each of those scores would be weighted by the composite rank, for a total sum of 3.71. Now, suppose candidate Y declares a 9, 7, and 5 for the respective categories. Candidate Y would then have scores of 30.3, 0, and 0, with a final weighted sum score of 13.6, and thus losing the election. Now, even though candidate Y is right with the mode on two issues, the stance on Guns drives candidate Y away from public preference since so many of the public weigh Guns as the most important issue.
One nice thing about this method is that preferences can be easily aggregated to any level of voting; nationwide, statewide, or district-wide. So, a minority opinion in a local preference setting may still have significant identification in a national setting, or vice-versa.
This is only a simple example. It does have flaws, i.e. there is no enforcement mechanism for candidates to truthfully state their preferences, and does not effectively screen people who might have socially awkward behaviors that prevent them from serving in pubic office.
What it does do, and I think this is pretty important, is that it forces people to do some serious introspection about what kind of representation they desire, and then declare those preferences for a direction of policies. It places the burden of study equally on candidate and voter alike, because it forces both to examine each policy subject in the survey, rather than picking by name. Furthermore, there is no need to expend mass amounts of money campaigning, trying to persuade people for his/her vote.
________________________
You made a common mis-statement of Arrow’s Theorem when you said:
CORRECTION:
Ken Arrow showed that there is no social choice function BASED ON RANKED ORDERINGS that satisfies A PARTICULAR SET OF logical properties.
Score Voting (aka Range Voting) isn’t “the next best thing”. It does everything Arrow’s Theorem says no RANK-BASED system can. Because it’s NOT rank-based.
http://scorevoting.net/ArrowThm.html
Arguably the Gibbard-Satterthwaite Theorem and the Simmons-Smith Theorem are much more important than Arrow’s Theorem, but Arrow’s Theorem receives a lot more attention because Arrow won a Nobel largely on the basis of “his” theorem (which is just a formal stating of what had been long known in voting theory).
http://scorevoting.net/GibbSat.html
http://scorevoting.net/SimmonsSmithPf.html
This gets into a tangential issue, which is that the Nobel Prize is typically awarded in a way that has almost no correlation with actual merit.
Others (including myself) have proposed your system of mapping candidates in “issue space” and determining the voter utilities for the candidates in that manner. That is actually what is done in Warren Smith’s Bayesian Regret calculations which constitute the most noteworthy argument for the superiority of Score Voting.
The problem with doing this in real life, however, is that one has to arbitrarily decide which issue dimensions will exist, and how much voters may care about relative distances in the various dimensions. In the Bayesian Regret calculations, this isn’t a problem because you are using this model to CREATE the voters’ utilities, so you KNOW what those utilities are — in essence you are an omniscient being in this digital simulated universe. In real life, that’s not the case. And the difference between your MODEL of voters’ issue dimensions, and the actual dimensions on which they are operating (and the weight they put on distances in the various dimensions) is guaranteed to be SIGNIFICANT.
So this system, while academically interesting, seems obviously to entail a huge amount of regret, probably far beyond what Score Voting (and even other commonly proposed alternatives) incur.
In summary though, I must thank you for this thoughtful post on a very under-appreciated issue. If you want to join the Election Science Foundation in its quest to improve democracy (and even just for the academic joy of discussing these sorts of issues) your help in our incorporation process (becoming a non-profit organization in the near future) would be much appreciated.
Best regards,
Clay Shentrup
The Election Science Foundation
Clay,
That was a thorough response. I had no idea that there was even a set of Bayesian Regret Calculations, and I am a semi-bayesian econometrician!
I appreciate the clarification on Arrow’s Theorem. To be honest, Social Choice Theory is not my strength and this post is more of an armchair comment. I am aware of the work of Donald Saari, who also had issue with Arrow’s Theorem. Saari tends to be a supporter of the Borda Count. I still think people are poor mappers, when it comes to mapping social/political preferences onto a single candidate, and it would be interesting to see how outcome might change under a scoring system when voters are not voting for people, but declaring preferences blindly.
This is certainly reaching for the obvious, but isn’t it highly relevant to consider truth-telling? If anonymous candidates were simply filling out a form for their preferences, the probability of lying seems fatally high for this to be an acceptable plan. The voting public has no reasonable way to verify the validity of any of the opinions–no voting records, no past statements, no indication of character, no opportunity to be cross-examined in debate, etc…
Honestly, the stated ballot issues of a candidate mean much less to me than whether or not I find myself believing the words coming out of their mouth when I see them interact with the public.
Then again, the purpose of the post may well be a thought exercise in voting and economics, not a political reality exercise.
Scott,
You’re right. Truth telling is an important part. But, to what advantage does a candidate aspire if the candidate does not know the population preference? Politicians can do polls and focus groups to judge how people react to them/their message. But, the only thing candidates can do is put together their own position surveys and sample people. That is the only way they would be able to gain information, and thus mis-represent their true convictions on a candidate form. But, the sampling would be woefully incompetent compared to a nationwide polling. One could also easily indicate that it would be to voters’ advantage to misrepresent their preferences on any polling sheet, negating the only informational advantage a potential candidate would have. Thus, the best response of a candidate is to truthfully represent his/her preferences.
Why would a voter gain an advantage by misrepresenting their preferences in a poll, outside of the sheer exhilaration of lying to a automated recorder?
I am actually being genuine in my question there–not cynical; I just don’t recall any voting games where voters stand to gain by not truth-telling.
Sorry, Scott. I have been ignoring you while cutting my teeth at bcc.
I guess the only utility gained by a voter for misrepresenting preferences on an unofficial preference polling is he/she knows a candidate basing his/her opinions off of a sample poll will be woefully misinformed. I know I would be happy to do that.
Scott B.,
The Bayesian Regret calculations I mentioned incorporate “ignorance factors” which are meant to account for the disparity between a voter’s assumption of a candidate’s value, and the real value. So maybe you love a candidate, but it’s because you don’t know that he regularly cheats on his wife or is taking money from Big Oil or whatever. It’s not a perfect way to simulate that, but the fact that the results are pretty consistent even as you widely vary the ignorance factors is noteworthy.
Also there were sincere and strategic voters, in incremental ratios from 0%-100% to 100%-0%.
I agree with you that a candidate’s sense of sincerity can have as much or more weight than his stated positions on issues. That’s why I looked pretty favorably at both Ron Paul and Barack Obama, despite their very different political views. They both seemed inspiring because I believed them more than many other candidates. Though Obama is now testing my patience.
Fletcher,
Yup. Quite right. Since voters have to base strategy off who the perceived front-runners are, it can be good to confuse your opposition by lying in a poll. There is significant evidence that people lie in polls. Sounds bizarre, but it happens — regardless of WHY it happens.