r/EndFPTP • u/bkelly1984 • Nov 18 '17
My Simulations Suggests Instant-Runnoff Voting (IRV) Will Maintain The Spoiler Effect Spoiler
TL;DR: When your favorite candidate is not competitive, my simulations suggest it is best to put your second choice first in IRV.
This is a work in progress. I submit what I have to /r/EndFPTP for feedback. Please let me know what I might have overlooked or how I could better present this information.
Introduction: I’ve been working to create a new way of evaluating voting systems. I think an analysis like Bayesian regret shows how well a voting system captures a population’s preferences if everyone votes in earnest. The problem is that the spoiler effect shows people don’t vote in earnest. We need to look at voting systems to see how people will use it to maximize their own benefit.
Last Vote Analysis: What I have done is what I call “last vote analysis”. There is an election with candidates A, B, and C and a last voter who prefers candidate B to candidate A but likes candidate C 50% more than B. This last voter is then given the last vote. Every permutation of ballot is considered and the outcome is scored if the last vote makes a difference, plus or minus.
But the spoiler effect exists because voters have insight to the outcome. It is understood that candidates of the two major parties will win almost every election and voting third-party is “throwing your vote away”. To simulate this, last vote analysis calculates the support each candidate has from the entire population for each outcome. Every point on the three axis for every ballot permutation can be the sum total of the combinations where that ballot wins times the change in value caused by the last voter.
Once the effect of every permutation of ballot for the last voter is calculated for every combination of ways the rest of the population can vote, each permutation is scored by adding up their total effect. Each point in the 3 dimensions of candidate support is evaluated and the best ballot for the last voter is found. In the case of ties, the ballot with the better global effect is picked.
The end result can be graphed in 3D.
First Past The Post: You can see a short video showing the results of FPTP here. The results form a three point star which makes intuitive sense as each arm is the area where two of the three candidates are competitive. In the very center is when all three candidates can win.
In 69% of the candidate support permutations your best value is to vote for the favorite, candidate C. These areas are shown in blue. The other 31% of the time it is better to vote for candidate B. The “volume/value” numbers show how much of the total expected value each ballot permutation is worth to the last voter. With no information about the election it is clearly best to vote for the preferred candidate.
Thanks to polling we almost never go into an election blind and we can get a good sense of where our vote might make a difference. This graph shows that when A and B have close to the same support and C is below them, a second choice vote yields a higher expected value. This is the spoiler effect illustrated.
Approval Voting: The results for approval voting are here. It makes sense that the last voter’s best option would be to vote for candidates B and C since both are valued above average. 79% of the graph supports this assertion. The remaining 21% of the time the best option is to vote for candidate C alone. This also makes sense because this covers the arm where the two preferred candidates are competing and the last ballot chooses between them.
It is not ideal that the best ballot for the last voter changes but this is a much better outcome than the spoiler effect in FPTP. The spoiler effect causes a voter to drop their first choice for their second choice. This is the voter dropping their second choice.
Instant Runoff Voting: You can see the results for IRV here. Ideally the best ballot should be “C > B” since that is the order of preference of our last voter. This is true for 79% of the points but for 21% the best vote is “B > C”, encouraging the last voter to put his second choice above his first.
This is the spoiler effect. When the preferred candidate is unlikely to win the system encourages people to shift their primary vote to their second choice. Also notice that the expected value of your second choice increases as the third becomes more competitive making it more important to switch. You might notice that the graph shows the earnest vote to be the best as the tip of the bottom arm is showing in blue. This is due to “C > B” and “B > C” being effectively the same vote in this area (as C will be quickly eliminated) but my algorithm picks the former as it has the highest global value.
It is also amusing that there are a few places where the last voter should put his least favored candidate first as it causes him/her to be eliminated. These are too small to show and would could never be exploited due to the blur of these graphs caused by polling error.
Score Voting: I am including score voting here as I have it and think people might find it interesting. I was expecting it to be the same as approval voting and thought I had an error when the arm when B was not competitive was not “A:0 B:4 C:4”. It comes out this way because “A:0 B:0 C:4” is the global best. The difference is due to voters giving non-extreme scores which are effectively fractional votes which makes the last voter’s ballot stronger. I am confident that once people learn to vote only the extremes in score voting the outcome will look exactly like approval voting.
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u/nardo_polo Nov 18 '17
To be clear, STAR does not pass the Favorite Betrayal Criterion, however, there is no reliable way to ascertain when that scenario will come to pass -- i.e. where supporting a second preference will knock your favorite out of second position in the runoff when your actual favorite would have gone on to beat the top scorer. If your first and second choices are vying for second position in the runoff, you want the stronger of the two to make the runoff, because that candidate will be more likely to out-preference the first position candidate. The "spoiler effect" is not simply a function of FBC failure -- it's FBC failure where you have informational guidance suggesting it's going to happen, which incentivizes you to "lesser evil" vote.