The day FairVote decided to vote on lunch
Tuesday lunch is a well-established tradition at the FairVote office here in Takoma Park. Each Tuesday, FairVote buys lunch for its employees, and it’s a perfect time for informal discussion and debate. Today was actually my last one, since my internship ends at the end of the week, but that is not my point.
Today, we could not decide on what to order and realizing that we are the voting system experts, we thought it would be great to cast votes before making any decision. So here were our candidates: Chinese food, Middle Eastern food and Pizza. Only one of them could win.
The main issue was: which system should we use, so that we get fair results? Different systems can indeed get different winners and this was a great opportunity to test their fairness and impact.
IRV |
Range Voting
|
First-Past-
|
Top-two
|
Condorcet Method |
|
Neal |
1- Pizza 2- Chinese 3- Middle Eastern |
Pizza: 10 Chinese: 0 Middle Eastern: 0 |
Pizza | Chinese |
|
Adam |
1- Chinese |
Pizza: 0 Chinese: 10 Middle Eastern: 0 |
Chinese | Chinese | |
Pauline |
1- Middle Eastern |
Pizza: 7 Chinese: 0 Middle Eastern: 10 |
Middle Eastern |
Middle Eastern |
|
Rob |
1- Middle Eastern |
Pizza: 5 Chinese: 0 Middle Eastern: 10 |
Middle Eastern |
Middle Eastern |
|
Amy |
1- Chinese |
Pizza: 0 Chinese: 10 Middle Eastern: 0 |
Chinese | Chinese | |
Winner |
Chinese Food |
Pizza
|
Tied Between
|
Chinese Food
|
No winner: tied
|
Because we were only five voters, the potential for tied results was high. And, even if there are different methods to decide who the winner should be in the case of tied results (based on the age of the candidate, or on a runoff between the top two candidates for instance), I thought that it would be more interesting to keep them tied, as a testimony of how split our votes were today.
In the case of the traditional system of first-past-the post, voters chose one candidate and the one with the most votes won. No choice received a majority of the vote, which means that resolving the tie results would not make a majority of the voters happy about the results. In either case (Chinese Food or Middle Eastern winning), 60% of the voters did not choose that possibility, which does not seem fair.
In the case of a top-two runoff, Neal was the tiebreaker: his first choice was out of the game, so he had the opportunity to refine his preference by choosing between Chinese food and Middle Eastern food. In that system, one choice had to win a majority of the vote, which seems pretty fair.
Then we had instant-runoff-voting (IRV), where voters ranked their choices according to their preferences. In the first round, Chinese Food and Middle Eastern Food both received two votes, and Pizza one vote. No choice got a majority, so Pizza was eliminated because it had the fewest votes. However, since Neal had expressed a preference by putting Chinese food as his second choice, the instant runoff determined that Chinese food now had three votes and Middle Eastern food, two. Consequently, Chinese food won a majority of the vote and was declared the winner.
Another method that we thought to use was range voting. With that method, voters had the possibility to score each of the candidates from 0 to 10. We added up the scores and the candidate with the most votes, Pizza, won. This system is worthy of note, because it enables voters to have a strategy: if you really want your candidate to win, you have an incentive to give him/her the maximum score and to give the minimum score the others. It is also interesting to see that Pizza won in that case: it was the preferred candidate of only one voter, but a good compromise candidate. However, Adam and Amy obviously both voted strategically, which makes it a bad system to use: we cannot make sure that people will vote sincerely.
Finally, the Condorcet method ended up with tied results. However, it is an interesting way of electing someone, since the winner would be the candidate whom voters prefer to the other candidates, when compared to them one at a time. This means that the winner would be the most preferred candidate overall, compared to the one being the first preference of most of the voters. This is a way to get the best compromise candidate.
So, there is obviously no right result, rather results that make a majority of voters happy or not. We went with instant-runoff-voting because we are convinced that it is the fairest system, were happy with Chinese Food and had a great Tuesday lunch!
Comment on The day FairVote decided to vote on lunch
Current Discussion
-
nicePosted by cheap vps, 2010-11-02 22:48:10 (1 year ago)
-
Looking at Clays X/Y/Z example -- note that if *all* the Z voters had accurate information and a desire to vote strategically, this information would probably be known -- in which case the Y voters could still cause Z to lose to (their slightly-preferred) X by just voting honestly -- let alone tactically on the assumption that Z is now a front-runner. So yes, it is possible for a strategic voter with perfect information to alter the result, but not easily.Posted by JimJ, 2010-05-26 08:55:36 (2 years ago)
-
Well, what would be a very interesting proposal would be the following. * Condorcet method for all elections * If no candidate has the most wins, the winner will be the one with the most overall votesPosted by Derek, 2010-05-22 12:51:07 (2 years ago)
-
I agree with you that it doesn't make much sense to promote Condorcet methods in general because of the possibility of a circular tie. Therefore, I always recommend to promote a concrete Condorcet method rather than Condorcet methods in general. To be more concrete: I recommend the Schulze method (http://en.wikipedia.org/wiki/Schulze_method). This method also satisfies the mutual-majority criterion, the Condorcet-loser criterion, the independence of clones criterion, and the monotonicity criterion; these criteria are considered important by FairVote (http://archive.fairvote.org/Single%20winner%20voting%20method%20chart.pdf).Posted by Markus Schulze, 2010-04-29 00:33:17 (2 years ago)
-
I apologize for perhaps over-posting here, but I just keep noticing more important things to learn from this election.
If you Pauline, or Rob, had insincerely/tactically ranked pizza in first place, then Middle Eastern would have been eliminated, and pizza would have won. There was ample opportunity for tactical voting here; only perhaps you couldn't exploit that since you didn't have pre-election polling.
If this had been a real political election, and you had seen a pre-election poll that showed Chinese being preferred to Middle Eastern by 60% of the voters, and pizza being the first choice of only 20% of voters (compared to 40% for the other two "candidates"), then you would have easily been able to deduce that it was "throwing away your vote" to put Middle Eastern in first place. Bloggers and televised pundits would have made note of this, effectively treating Middle Eastern as something of a Ralph Nader (a spoiler that you don't want to waste your vote on). You would have had sound rational justification for strategically insincerely ranking pizza in first place. And even if you didn't actually do it, lots of other voters would do it. As a matter of fact, they do.
Posted by Clay Shentrup, 2010-04-28 23:23:32 (2 years ago) -
Jack,
It is indeed interesting to look at rates of approval-style and bullet voting with Score and Approval Voting.
It is unfortunate that we can't analyze ranked ballots in the same way. We can only look at statistically significant trends in large data sets. But that's extremely difficult because the individual ballots from most IRV elections are never made public.
Posted by Clay Shentrup, 2010-04-28 20:36:01 (2 years ago) -
This is a great post. It's interesting to see who "plumped" under range and who didn't, for example. Keep up the good work, guys!Posted by Jack, 2010-04-28 19:04:57 (2 years ago)
-
Pauline said:
Range voting satisfies the average voter when IRV satisfies a majority of voters. Here is the difference and this is why we used IRV.
A majority of voters preferred pizza to Chinese food. So Score Voting better satisfied the average voter, and the majority of voters.
IRV does not guarantee a "majority winner"; it merely guarantees that the winner is preferred by a majority to at least one opponent. Here's a simple example proving that.
% of voters -- their rankings where "X > Y" means "prefers X to Y" 35% A > C > D > B
17% B > C > D > A
32% C > D > B > A
16% D > B > C > A
Source: http://scorevoting.net/CoreSuppPocket.htmlCandidate B wins with IRV, but a huge 67% majority of voters would rather have candidate C than candidate B. And candidate C received nearly twice as many first-place votes as candidate B, 32% to 17%. And an even larger 83% super-majority of voters would rather have candidate D than B (and D got just a little fewer first-place votes than B). So the claim that IRV "elects majority winners" is seriously misleading.
Also there's lots of opportunity for strategic manipulation here. Say the first row of voters insincerely ranks C or D in first place. Then they can get a better result by causing C or D to win instead of B. So it's misleading to suggest that tactical behavior is a weakness for Score Voting. It's not. It's a strength. This has been understood for a decade or more by mathematicians who study voting methods.
This election also demonstrates the fallacy of attacking a voting method simply because it might be more prone to tactical voting. Apparently some of the Score Voting ballots were tactically exaggerated. Say we assume for the sake of argument that the IRV ballots were 100% honest, with no tactical behavior. Then Score Voting still picked a better outcome that was more satisfying to the majority of voters than the IRV outcome -- even in spite of that strategic voting.
More realistically, lots of IRV voters are strategic, as evinced from decades of IRV use in countries like Australia. In that case, the tendency for Score Voting to pick better outcomes than IRV is even greater.
I believe that FairVote promotes IRV because they see it as an incremental "stepping stone" to the STV system, which is a proportional representation method. In fact FairVote began as "Citizens for Proportional Representation". Thus they promote IRV regardless of any contrary facts about it, because all that really matters to them is getting proportional representation via STV, like they have in Australia's Senate. The evidence for this "theory" is overwhelming.
Posted by Clay Shentrup, 2010-04-28 16:07:23 (2 years ago) -
Thanks for coming by the FairVote blog and commenting. As I said in my post, “there is obviously no right result, rather results that make a majority of voters happy or not”. But, let’s consider your arguments.
If we go back to our example of range voting:
- Amy really wanted Chinese food (she did not rank any other candidate in the IRV) and was sincere in her scoring.
- Adam really wanted Chinese food and knew that if he had given any point to one of the other candidates, he would have reduced his chances to get Chinese food.
- Neal also knew exactly what he wanted: pizza. And only scored pizza so that he would not favor any other candidate that he did not like.
- Rob and I wanted Middle Eastern, but would have been fine with pizza so we gave a score to pizza. That was logical with our preferences expressed in the ranking. But we both knew that Adam and Amy wanted Chinese food, so we did not score Chinese food to raise our chances to get either pizza or Chinese food.In that case, we would have been happy with pizza, since it was a good compromise candidate for a majority of us. This is why I wrote that range voting is an interesting system. You can get results that would make a majority of voters happy. However, there is an obvious possibility to play with the system.
With range voting, the candidate with the most points wins. But the winner does not have to be preferred by a majority of voters and those on the tactical fringe can overrule the majority of voters when a majority votes sincerely and the minority votes tactically.
Consider a new simple example: 100 voters can score two candidates, from zero to 100. Those two candidates, A and B, are mediocre according to the voters. 98 voters dislike Candidate B more than Candidate A: to express their distaste, they give one point to Candidate A and none to Candidate B. The two remaining voters do prefer Candidate B, even if they do not like any of the two candidates. Those two voters want to be tactical and give 100 points to Candidate B and 0 to candidate A. In the end, B beats A with a landslide of 200 to 98, despite that fully 98% of voters preferred Candidate A.
This of course is exaggerated for the purpose of my argument, but it shows how tactical fringe can overrule a majority of voters. Furthermore, the more candidates you get, the highest incentives to tactical calculation get: the winner does not even need to be the first choice of anybody. Last, but not least, voters do not score their preference the same way: the same way you’ve had teachers more or less strict on their grading, you’ve got voters more or less strict on their scoring: scoring is not universal and range voting gives voters an incentive to exaggerate their score so that their favorite candidates have a better chance, and their least favorite candidates are more likely to lose.
Furthermore, a voter has to make a decision: do I care most about what I want (in which case I give that choice the most points possible, and nothing to anything else), what I like the least (in which case I give the most points possible to all other choices and nothing to that choice) or do I not really care? That’s not easy to answer, especially when you don’t know what other people are going to do.
We know not everyone is going to agree, but this is why FairVote believes that IRV is a better solution. With IRV, the winner will have received a majority of the vote (60% in our case), have a core support and voters are unlikely to be insincere: since their preference is going to influence the rest of the instant runoffs, they are likely to put their first choice, first, their second, second etc.
Range voting satisfies the average voter when IRV satisfies a majority of voters. Here is the difference and this is why we used IRV.
Posted by Pauline Lejeune, 2010-04-28 11:25:01 (2 years ago) -
Sorry, one last comment. :)
60% of the voters were happier with the results of Score Voting than you were with Instant Runoff Voting. So the majority preferred Score Voting here.
And that's in spite of the (alleged) fact that IRV ballots were honest while some Score Voting ballots were insincerely exaggerated. This attests to the superiority of Score Voting in measuring voter sentiment.
Posted by Clay Shentrup, 2010-04-27 23:48:44 (2 years ago) -
It would be interesting to see all of your SINCERE scores. Then we could calculate the average satisfaction of the group for each choice, and see which method(s) made the most pleasing choice here.Posted by Clay Shentrup, 2010-04-27 23:20:45 (2 years ago)
-
Your example with Score Voting (aka "Range Voting") and strategic behavior by the pepperoni lover is simply misleading. Here's a concrete example to prove it. Say we have these three groups of voters (keeping it simple for the readers' sake) followed by their sincere preferences for candidates X, Y, and Z as satisfaction ratings on a 0-10 scale.
33% of voters think X=10, Y=9, Z=0
32% of voters think Y=10, X=1, Z=0
35% of voters think Z=10, Y=9, X=0The sincere average scores are:
X = 3.3 + 0.32 + 0 = 3.62
Y = 2.97 + 3.2 + 3.15 = 9.32
Z = 0 + 0 + 3.5 = 3.5Clearly the average voter would be much more satisfied with candidate Y than with the other options. And slightly more satisfied with X than with Y. But if these voters use sincere rankings, then IRV elects X. (Y is eliminated first, then X defeats Z head-to-head.) But say these voters use tactical Score Voting. Will they get a worse result as Pauline suggests? Nope. The "front-runners" are X an Y, and the tactic with Score Voting is to give a 10 to your favorite front-runner (and to every candidate you like better), and a 0 to the other front-runner. So the above scores become.
33% X=10, Y=0, Z=0
32% Y=10, X=0, Z=0
35% Z=10, Y=10, X=0Candidate Y picks up 10's from 67% of the voters, and handily defeats X. Score Voting gives a better result. While it's true that the Z voters could elect Z by strategically giving Y a 0, that is both extremely unlikely (it requires nearly 100% of them to use this tactic), and can also happen with IRV, producing even worse results. In fact there is a way to look at the average voter satisfaction that voting methods produce, based on a statistical averaging of these scenarios, in a way that's proportional to their real-life frequency of occurrence. It's called Bayesian Regret, and it's explained here: http://ScoreVoting.net/BayRegDum.html Score Voting has substantially lower Bayesian Regret than IRV. It picks better winners more often, even with strategic voting taken into account. And it's simpler and has lots of other benefits, like helping to break out of two-party domination, and creating a feasible step forward to proportional representation.
Posted by Clay Shentrup, 2010-04-27 22:11:36 (2 years ago) -
>range voting... This system is worthy of note, because it enables voters to have a >strategy: if you really want your candidate to win, you have an incentive to give >him/her the maximum score and to give the minimum score the others. It is >also interesting to see that Pizza won in that case: Most voting systems enable voters to have strategy - most definitely including IRV (eg bury frontrunner candidates other then your favorite of the frontrunners). Your comparison between voting systems is deceptive since you only voters use strategy in one system.Posted by AllAboutVoting, 2010-04-27 16:19:19 (2 years ago)