The reason I didn’t mention that, is because there are two related constraints a voting system can satisfy:
- Later no harm, which basically states that once you’ve ranked something, ranking additional items behind it cannot hurt the chances of the items you’ve already ranked.
- No favorite betrayal, which basically states that ranking something higher, should not hurt the chances of it being elected.
Unfortunately it’s widely accepted that these two properties are mutually exclusive, so while IRV “passes” Later no harm, it fails No favorite betrayal. The other options all go one way or another on that, with the only really novel one being 3-2-1 which technically fails both later no harm and no favorite betrayal, but it appears the properties of it suggests that it’s unlikely it’ll fail either of them (but it could).
I didn’t call out because I consider these two properties to be largely the same in terms of impact. Both of them mean that, it’s possible, for an honest ranking to hurt the chances of your top choice, just through different mechanisms.
It appears that you think later-no-harm is an important property, but that you don’t really care about no-favorite-betrayal, and my question would be why? I don’t mean that snarkingly, I’m curious because as I mentioned above, they both mean that an honest ranking will hurt the chances of your top choice, so why is one mechanism for that to happen the end be all?
Just for completeness:
- IRV: Passes later-no-harm, Fails no-favorite-betrayal
- Condorcet: Fails later-no-harm, Fails no-favorite-betrayal
- I had actually forgotten when I wrote the above that Condorcet also fails both of them, although it (well the shchulze method at least) passes another, similar thing which all the other systems (except maybe 3-2-1, I’m not sure on it) fail, which is Strategy Free, which basically says that if everyone votes honestly, than the choice the majority prefers will win.
- Approval: Later-no-harm and no-favorite-betrayal doesn’t apply since there is no ranking to be done, however it suffers from a conceptually similar effect of later-no-harm where approving your 2nd or 3rd choice can help them win over your first choice. It passes a conceptually similar effect to no-favorite-betrayal where approving your first choice cannot hurt it.
- STAR: Fails later-no-harm, passes no-favorite-betrayal
- 3-2-1: Fails later-no-harm, fails no-favorite-betrayal, appears that as a benefit it makes it exceedingly unlikely either case actually happens.
I think it’s probably a mistake to focus too much on specific criterion here, because as a number of impossibility theorems have stated, it’s basically impossible to get them all. Looking at the general quality of the outcomes is probably a far better mechanism than trying to pick which (roughly equally important/bad) criterion we’re going to care about, and which we’re not.
Better I think to look at the actual results the variety of elections give.
One source of that is looking at how well different methods fair in voting simulations like those found at Voting Simulation Visualizations. In every one of the simulations there, IRV’s position is basically “better than plurality, but worse than everything else”, with a special mention of Borda which has it’s own brand of strange results when it comes to split votes.
Another mechanism we can look at is Voter Satisfaction Efficiency (VSE) (sometimes Voter Satisfaction Index or social utility efficiency), which is basically a measure of how well does a particular system fair at giving the voters what they want, under certain conditions (100% honest votes, 100% strategic votes, and in between). In these systems generally you consider drawing names out of a hat to be 0%, and being able to read people’s minds and magically select the perfect candidate to be a 100%. You can get some information at Redirecting to http://electionscience.github.io/vse-sim/VSE/.
One interesting graph from electology would be:
Which graphs the variety of options under the different scenarios (If you go to the website, and click the graph there is an interactive version).
The scores for IRV range from ~79% to ~91% depending on whether how honest people are being in their voting.
The scores for Ranked Pairs (the simplest way to determine a Condorcet winner) is 87%-98%.
The scores for Schulze are 80%-90%.
Approval is a bit hard to model as a single system, because the underlying question becomes, at what level of utility do you approve of a choice vs disapprove. The above graph has two models, one is where you approve any choice that has “above average” utility (aka IdealApproval) and another where you assume 60% of voters are going to bullet vote and select only their preferred choice, and 40% will vote as in Ideal Approval:
For Ideal Approval, the score range 84%-94%.
For 60% Bullet Approval, the score range 85%-95%
For score/range methods (aka rate choices 0toN, winner is highest average rating) no matter what N is, the range is 84% to roughly 97%, though the larger the N is, the slightly higher the top end becomes.
Star voting with a 0-10 rating has a range of 91%-98%.
3-2-1 has a range of 91% to 95%.
If we say that we expect people to only vote honestly, and are unlikely going to employ any sort of strategic voting, that gives us numbers like:
- IRV: 91.3%
- Ranked Pairs: 98.8%
- Schulze: 98.8%
- Ideal Approval: 87.5%
- 60% Bullet Approval: 89.9%
- Score/Range with a 0-10 rating: 96.8%
- Star voting with a 0-10 rating: 98.3%
- 3-2-1: 94.3%
Neither of these types of methods of evaluating voting systems are slam dunk, but I think it’s generally a good thing to try to select an option which:
- Has a reasonable set of outcomes in voting simulations like on Voting Simulation Visualizations without any surprising behavior.
- Has a high VSE, particularly when people are honest voting (since we expect most, and maybe all people to vote honestly).
- Does not have a scenario with a low VSE in case people decide not to vote honestly.
Of those, Schulze/Ranked Pair gives the highest satisfaction when everyone is voting honestly, and it has no weirdness in the voting simulations, however it has potential for strategic voters to bring the overall VSE down.
Approval voting has roughly the best voting simulations, but it has the interesting property that people are generally happier with the election results when they’re not voting honestly, then when they are, and when voting honestly it’s generally worse than honest votes with IRV (although IRV is worse in the presence of tactical voting).
Star and Range voting have the second highest satisfaction (with Star voting basically being inline with RP/Schulze), but neither one has been graphed by Ka-Ping Yee and I don’t have similar graphs handy elsewhere. Range voting’s bottom end of the VSE is lower due to issues where a one-sided tactical voting can have an outsized impact on the election, whereas Star voting doesn’t suffer from that nearly as badly (Star voting’s improvement over range voting is specifically to eliminate that).
3-2-1 also isn’t graphed be Ka-Ping Yee, and I also don’t have similar graphs handy elsewhere. It has the interesting property that tactical voting has very minimal impact on how satisfied people are with the outcome (IOW, the grouping is tighter in the graphs), but it also has people happier when they are strategic voting rather than honest voting, and it’s VSE is generally lower than other options.
Given all of that… My personal opinions are:
- IRV can be ruled out because it performs poorly in simulations and it’s “bottom” end of VSE is one of the lowest we’re looking at.
- Approval voting can be ruled out because VSE numbers are less great than the other options, and generally having people happier when tactical voting vs honest.
- As much as I like STAR/range voting, I’d say we can rule it out because we don’t have graphs available to show how it holds up in a variety of situations (though I believe it holds up well). It’s also possibly a harder sell to get people to rate their choices than rank them.
- Similarly to STAR/range voting, I don’t have graphs for them and I’m not honestly sure how it performs. It also has the property that generally folks are more satisfied with tactical votes than honest votes (though the grouping is so tight it probably doesn’t matter) and overall people are just less satisfied with it than other options, so I think we can rule it out.
That leaves some method of Condorcet, which when everyone is voting honestly has the highest VSE, which makes some amount of sense since the Condorcet winner is the winner that everyone would pick in every two way match up. The difference between the Condorcet methods ultimately comes down to what happens when there isn’t a Condorcet winner.
Specifically with regards to IRV vs Condorcet, I’d quote Wikipedia’s comparison of IRV and Condorcet methods:
Many proponents of instant-runoff voting (IRV) are attracted by the belief that if their first choice does not win, their vote will be given to their second choice; if their second choice does not win, their vote will be given to their third choice, etc. This sounds perfect, but it is not true for every voter with IRV. If someone voted for a strong candidate, and their 2nd and 3rd choices are eliminated before their first choice is eliminated, IRV gives their vote to their 4th choice candidate, not their 2nd choice. Condorcet voting takes all rankings into account simultaneously, but at the expense of violating the later-no-harm criterionand the later-no-help criterion. With IRV, indicating a second choice will never affect your first choice. With Condorcet voting, it is possible that indicating a second choice will cause your first choice to lose.
[snip]
There are circumstances, as in the examples above, when both instant-runoff voting and the ‘first-past-the-post’ plurality system will fail to pick the Condorcet winner. In cases where there is a Condorcet Winner, and where IRV does not choose it, a majority would by definition prefer the Condorcet Winner to the IRV winner. Proponents of the Condorcet criterion see it as a principal issue in selecting an electoral system. They see the Condorcet criterion as a natural extension of majority rule. Condorcet methods tend to encourage the selection of centrist candidates who appeal to the median voter.