On May 20, 2004, at 4:46 PM, Ken Johnson wrote:
I think it's simply the case that with 1 issue, all voters' CR profiles are precisely correlated (i.e., any two profiles differ only by a multiplicative scale factor), so all these methods become equivalent.Date: Wed, 19 May 2004 23:24:29 -0700 From: Bart Ingles <[EMAIL PROTECTED]>
... In your 10 candidate, 1 issue trial, are you able to account
for why sincere CR, exaggerated CR, Condorcet, Borda, IRV, and Plurality
all yield exactly the same average across 100,000 elections? It looks
like top-two Runoff is within 0.1% of the same score.
This doesn't make sense to me. If a voter has a random preferred stand on an issue, and a candidate has a random position on an issue, then every voter should have a different opinions of the candidates.
In my simulation I skipped the "issue" problem and designed voters to have direct utility for each choice. It was a uniform distribution, perhaps a normal distribution would have better simulated a multitude of issues combined in subtle ways.
Here's what I get for a similar test configuration: running work set 10 candidates, 100 voters, 100000 trial elections, +/- 0.000000 confusion error, 15 systems
| Name | Avg. Happiness (higher better) | Reliability Std. (lower better) | Consensus Std. (lower better) |
|---|---|---|---|
| Max Happiness | 0.0888975746 | 0.0338515816 | 0.570981684 |
| One Vote | 0.0465569835 | 0.0522550793 | 0.590699266 |
| Instant Runoff Vote | 0.0691708706 | 0.0449100316 | 0.58041986 |
| Acceptance Vote | 0.076919622 | 0.0412060098 | 0.570201211 |
| Rated Vote, raw | 0.0888975746 | 0.0338515816 | 0.570981684 |
| Rated Vote, equal sum | 0.0874381314 | 0.0348641877 | 0.571236063 |
| Rated Vote, maximized | 0.0885278883 | 0.0341252313 | 0.57094033 |
| Rated Vote, 1..num choices | 0.0883559702 | 0.0342327482 | 0.571054417 |
| Rated Vote, 1..10 | 0.0883559702 | 0.0342327482 | 0.571054417 |
| Ranked Vote | 0.0848481788 | 0.0365165917 | 0.571332999 |
| Ranked Vote, no neg pref | 0.0814575574 | 0.0388052255 | 0.576437401 |
| Condorcet | 0.079960858 | 0.0387813296 | 0.572688295 |
| IRNR | 0.0833061568 | 0.0372725737 | 0.571565448 |
| IRNR, positive shifted | 0.0846562353 | 0.0365433369 | 0.561307907 |
| Random | 0.000203974106 | 0.0580343337 | 0.573728578 |
| Name | Avg. Happiness (higher better) | Reliability Std. (lower better) | Consensus Std. (lower better) |
I suppose it's similar overall, but I think I see more variation in the primary statistic "Average Happiness", which makes me wonder if there's some artifact in your simulator.
Brian Olson http://bolson.org/
