Range Voting

[kevin_standlee]

The folks advocating Range Voting contacted WSFS (actually, the WSFS webmaster, sfrose) lobbying WSFS to change its voting system from the Instant Runoff Voting system we currently use for site selection and the Hugo Awards. Sharon told them how our rules work and suggested that if they want to change them, they come to WSFS business meetings and propose and debate the changes there, like all other rule changes. The advocate's response, in my opinion, amounted to, "Our proposal is so obviously Right that we shouldn't have to do all that hard, expensive work. You should change your rules because we tell you to do so."

I often tell people who come to me with rules-change proposals, "If you think it's worthwhile, come and submit it yourself. I'll help you with all of the technicalities to the best of my ability, but you have to make your own case, lobby people yourself, and get the votes by convincing people." Most of the time, this discourages them -- democracy is hard work! But sometimes we get people who are willing to work and debate, and sometimes we even get workable changes and improvements.

WSFS rules are intentionally designed to be resistant to change; however, they can be changed if people work hard enough at it. But it's not enough to just lobby a Board of Directors or subvert the Chairman; you have to convince the members.

Comments

Re: Supermajority vote?

[kalimac.livejournal.com]

That chart is really baffling. What do those percentages mean? It's surely not the percentage of voters who get their preferred candidate. Is it the opinion poll results for satisfaction with the voting method? That doesn't look right either.

Re: Supermajority vote?

[thebrokenladder.livejournal.com]

I left a link to where it is described.

http://RangeVoting.org/vsr.html

Here's a quick example to explain it to you in a nutshell. We have voters V1 - V6, and candidates C1 - C5. Below is a table of the utility values from each voter for each candidate. Think of utility as "desire" or "happiness/satisfaction one would get by having that thing". These values are in "happiness units" of arbitrary magnitude. Don't worry that we can't objectively quantify that unit, because later we divide, which drops the terms out and leaves us with a unitless value - just a ratio.

C1 C2 C3 C4 C5
V1 2 30 -16 52 56
V2 24 30 10 60 30
V3 40 -8 -30 12 -18
V4 37 36 8 -28 -37
V5 -26 -28 -11 -28 8
V6 45 58 22 -4 55
UTILITY AVG. (U) 20.33 19.67 -2.83 10.67 15.67
BAYSIAN REGRET 0.00 0.67 23.17 9.67 4.67
VSR 100.00% 91.27% -203.49% -26.64% 38.86%
VSR = (U - average(U)) / (max(U) - average(U))

In this example, C1 produces the greatest happiness for the greatest number, with an average utility of 20.33. C3, on the other hand, produces a an average utility of -2.83, the lowest. But these numbers are like cubits, only comparable to each other, but not to numbers from other scenarios. To resolve that, we rescale the utilities, such that the voter satisfaction ratio of picking the ideal winner is a 100%, and the VSR of picking a random winner (just the average of all the candidates' utilities) is 0%. The formula is mentioned below the table. For the highest utility value, U = max(U) so we get 100% social utility efficiency.

If we test honest plurality voting here, C1 and C5 tie, 2-2. But say we use strategic plurality, where each voter strategically votes for his favorite between the two front-runners. Then C5 wins 4-2.

Now say we try range voting, using the standard definition of "honest" range voting, where each voter simply rescales his utilies to the specified range (0-10, 0-99, whatever). Then we get:

C1 C2 C3 C4 C5
2.50 6.39 0.00 9.44 10.00
2.80 4.00 0.00 10.00 4.00
10.00 3.14 0.00 6.00 1.71
10.00 9.86 6.08 1.22 0.00
0.56 0.00 4.72 0.00 10.00
7.90 10.00 4.19 0.00 9.52
5.63 5.57 2.50 4.44 5.87

C5 just barely beats C1, even though C1 produces a tremendously higher voter satisfaction ratio. Of course that's partly because I tweaked this example (starting with random values that I then tuned) to show examples where Range Voting can indeed pick a pretty poor winner. (note that some candidates have negative values, because they produce less satisfaction than what would be expected from picking a RANDOM candidate - a voting method that picked them regularly would be WORSE than drawing a name out of a hat, instead of better, defeating the purpose of democracy).

Now say I go in and randomly plug a bunch of numbers in for the honest utility values again.

C1 C2 C3 C4 C5
V1 25 55 7 20 45
V2 12 25 1 18 19
V3 16 16 8 17 6
V4 35 40 0 34 41
V5 2 21 11 19 35
V6 8 12 15 5 7
UTILITY SUM (U) 16.33 28.17 7.00 18.83 25.50
BAYSIAN REGRET 11.83 0.00 21.17 9.33 2.67
VSR -31.48% 100.00% -135.19% -3.70% 70.37%

I dispensed with negatives this time, just because it's easier to type a bunch of random positive numbers in quickly without putting thought into it.

Now let's see which winner HONEST plurality would pick.

C2 and C5 tie, 2-2. So if voters were strategic with plurality (voting their favorite between just those TWO) they'd get C2, by a 4-2 vote. Producing a VSR of 100%! What about "honest" (normalized) Range Voting?

C1 C2 C3 C4 C5
3.75 10.00 0.00 2.71 7.92
4.58 10.00 0.00 7.08 7.50
9.09 9.09 1.82 10.00 0.00
8.54 9.76 0.00 8.29 10.00
0.00 5.76 2.73 5.15 10.00
3.00 7.00 10.00 0.00 2.00
4.83 8.60 2.42 5.54 6.24 <-- Averages

It would also pick C2, by a hefty margin. And if C2 dropped out, it would elect C5. So, here strategic plurality has actually worked pretty well, and so has Range Voting. Now imagine taking these simplified spreadsheet examples, and using something like 20 different voting methods, and MILLIONS of elections, with 720 different combinations of election parameters (strategic vs. honest, ignorant vs. informed voters). That's how we got the results I present to you.

Clay

Re: Supermajority vote?

[kalimac.livejournal.com]

Next time you post a chart, could you put the preformatted text HTML tag around it? (the letters PRE in angle brackets) As it is they're all flush left and impossible to read. Thanks.

Re: Supermajority vote?

[thebrokenladder.livejournal.com]

Oh, sorry. Check this out:

http://spreadsheets.google.com/pub?key=pXPf6D8HwIWncwYJKKb4CcQ