[EM] cloneproof[strat2-revote]

[Jobst Heitzig]

Dear Warren!

> cloneproof[strat2-revote]
> 
> A voting method hereby is "cloneproof[strat2-revote]" if W'=W when:
> 1. We hold an election with strategic voters, electing winner W.
> 2. we add clones (perhaps multiple clones) of some subset of the candidates.
> 3. The voters re-vote in the new election, again acting strategically
> in the new scenario.  We get winner W'.

That is a very interesting concept! I still have some problem in grasping what exactly you mean by "acting strategically" since there is almost always a whole bunch of possible strategies which could seem worth trying, depending on what information you have about other voters' preferences, behaviour, and willingness to cooperate, and depending on how well you can organize complex voting profiles for a strategizing group. 

But we could certainly start by refining the definition to use one or other specific strategy, for example expected-utility-maximizing zero-info strategies.

By the way, my conjecture about this kind of strategy in DMC is that it is to submit sincere preferences and approve all above-expectation candidates, just as in Approval Voting. At least I think this is so when equal ranks were not allowed. With equal ranks allowed, I guess that for example in the three-candidate case with sincere preferences A>B>C and B's utility close to A's it could give greater expected utility when voting A=B>>C than when voting A>B>>C. Has anybody studied such a case for other Condorcet methods?

Jobst
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