[EM] Ruminations on strategy issues in IRV and Condorcet (was possible improved IRV method)
simmonfo at up.edu
Thu Jun 29 19:25:01 PDT 2006
Any time that IRV does not elect the sincere CW (when there is one) there is going to be a strong incentive for order reversal under IRV, except under the (non-existent) zero information case. [The only real life cases that exist in hot elections are the positive information and positive disinformation cases.]
Why is there an incentive for order reversal under IRV when the CW is not elected on the basis of sincere rankings?
Because the losing faction(s) on the opposite side of the CW from the IRV winner would rather have the CW than the sincere IRV winner, so they have an incentive to rank the CW ahead of their favorite.
On the other hand, Condorcet Compliant methods have divers ways of resolving cycles, which cycles can be created artificially by some non-CW faction that thinks it might have a chance of winning in the particular cycle resolution method that has been adopted.
It seems that to avoid significant incentives for order reversals the method must satisfy the FBC (Favorite Betrayal Criterion). Both IRV and proposed Condorcet methods fail even the weak version of FBC.
Mike Ossipoff's last thrust before he retired from this list was his (well considered) opinion that if a method is known not to satisfy the FBC, then many voters will panic and rank only perceived viable candidates in first place.
[That wouldn't be so bad if perception weren't so tricky in the face of all of the disinformation floating around.]
All known deterministic FBC proposals allow for equal ranking at the top, or make no instrumental difference in the top two ranks, i.e. the difference is expressive only, so all of these methods fail the Strong FBC.
The only known methods that satisfy the Strong FBC are non-deterministic, i.e. what Jobst and I call "lotteries," and most lotteries fail the FBC, too, though Random Ballot satisfies the Strong FBC.
IRV supporters like being able to rank Favorite strictly above Compromise with the illusion of optimality.
But that's all it is, an illusion of satisfying the Strong FBC.
The simplest deterministic method that satisfies the (weak) FBC is Approval.
In my opinion, more complicated methods based on rankings or ratings can justify their increased complication only by allowing the "Select from a Published List of Rankings or Ratings" option.
Also (in my opinion) Asset Voting is another method that is so inexpensive that it is worth promoting. It satisfies the Strong FBC when you take into account that you can write in yourself, and thereby represent yourself in the asset concentration process, if you are unwilling to delegate that role to one of the regular candidates.
Randomly chosen juries are another idea worth promoting in some contexts.
I used to believe that DSV methods would be the wave of the future. But DSV methods usually turn out to be either non-monotonic or non-deterministic. I'm more willing to give up determinism than monotonicity.
[From here on proceed with caution.]
Here's a some recent thoughts along these lines (only for those aren't afraid of weird thoughts):
The DLE (Democratic Lottery Enhancement) process is monotonic, in the sense that if ballot set B' improves candidate X's standing compared to ballot set B, then lottery L enhanced by B will not give X a better chance than lottery L enhanced by B'.
Furthermore, given L, your optimal ballot for enhancing L is your sincere ballot.
However, if you are told that the enhancement process will be iterated, then your sincere ballot is no longer optimal. In particular, if some lottery is iterated to equilibrium, i.e. to a fixed point of the enhancement process, then it may not be optimal to vote sincerely.
But what if the equilibrium were (perhaps by chance) the original lottery, so that no iteration was necessary?
Then it depends on whether or not you knew ahead of time that the original lottery would be chosen from the set of fixed points. If you knew that, then you might have enough information to vote insincerely in order to change the set of fixed points (to your advantage) from what their positions would be on the basis of sincere ballots.
If you could vote twice, once to help determine the equilbrium lottery, and then again to vote optimally once that lottery was determined, then it would be to your advantage to vote insincerely the first time and sincerely the second time, but then it would turn out that the supposed equilibrium was not really an equilibrium.
Ideally, the equilbrium lottery would be determined from a random sample of innocent voters who had no idea why they were being polled. Then they would have no reason to vote insincerely. Etc.
But if you polled only innocent voters, the sample would not be random.
This reminds me of the uncertainty prionciple of quantum mechanics and of Maxwell's Demon in thermodynamics. Here the demon would have to filter out the sophisticated voters and allow only the innocents to vote.
I suspect that most if not all DSV equilibria, deterministic or not, will suffer from this same complementarity problem.
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