a full understanding of optimal strategy is probably impossible.
I don't think a full understanding is needed. How about a Nash equilibrium for the students, given that the schools report their preferences honestly? No collusion allowed in this model, just each student choosing on their own. Charles Greathouse Analyst/Programmer Case Western Reserve University On Tue, Dec 9, 2014 at 2:18 PM, Warren D Smith <warren.wds@gmail.com> wrote:
You really can't say anything about strategic voting here? At all?
Let's suppose I receive 50, 75, or 90 utils for attending school A, B, or C respectively (or 0 for not attending any). At a minimum, I should rate A at 0 and C at 100 to maximize incentive to be assigned to the school of my choice. If I knew that C was extremely selective and I was unlikely to get in, it would be strategically sound for me to assign many points to it (rather than simply scaling up the difference) rather than honestly/naively reporting my true preference. Exactly how many points depends on the chance I think I'd get in, but it's not unreasonable to expect that I would want to assign 99 or 100 points to it.
On the other hand, suppose I would receive -10, -5, or 100 utils for attending A, B, or C (or 0 for not attending any). Then I should rate them at 0, 0, and 100 points, since I am truly indifferent to A and B (I wouldn't go if accepted).
A voting method that can't handle strategic voting is a bad method. Sure, we know complete strategyproof-ness is impossible (Gibbard 1973, Satterthwaite 1975) but that doesn't mean (1) that tactical voting doesn't exist or (2) that we shouldn't plan for it.
Charles Greathouse Analyst/Programmer Case Western Reserve University
--well, one can give anecdotal examples such as this, but a full understanding of optimal strategy is probably impossible. Further, usually in multiplayer games the "best strategy" involves collusions between large subsets of the players, which is kind of why you can't describe optimal strategy, they collude, they cheat on the collusions with other collusions, etc etc.
You can empirically try to reckon performance of these sorts of things by computer simulation, including (if you want) the players in the sim apply various strategic behaviors.
That was in fact exactly what I did in 2000 with single-winner voting methods, finding "score voting" aka "range voting" was the best of the methods in my (then) simulator.
I'm unaware of any sim-study of the current sort of problem (matching children to schools). Might be interesting to try to do one.
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