You wrote (Thu.Dec.9,04):
Am I correct in thinking that this meets the criteria mentioned above? Does this seem like a sensible way to do IRV-completed Condorcet in general?My answer to your first question is that it seems to me that it does, and it also seems to meet Minimal Defense. But it shares Condorcet (Winning Votes)'s zero-information random-fill incentive, which in my view is silly and unfair and therefore not really acceptable.Personally, I don't find that very disturbing. Silly, maybe, but not a serious problem. I'm guessing that most methods meeting the truncation resistance/SFC criteria will have this problem. Do you think that the truncation resistance criterion is misguided? I sort of go back and forth on it... sometimes I think it's quite important, sometimes I don't. I do think that it's more important that the random fill incentive, however.
truncation resistance: Define the "sincere top set" as the smallest subset
of alternatives such that, for each alternative in the subset, say x, and
each alternative outside the subset, say y, the number of voters who
sincerely prefer x over y exceeds the number who sincerely prefer y
over x. If no voter votes the reverse of any sincere preference regarding
any pair of alternatives, and more than half of the voters rank some x in
the sincere top set over some y outside the sincere top set, then y must
not be elected.
CB: To answer your question, I think that the Truncation Resistance criterion (as defined above) is desirable but not(from Steve Eppley's MAM site)
essential. If there is a random-fill incentive, then I think it is rendered pretty meaningless.
We know that is impossible to thwart sufficiently well-informed strategists, but quite easy for a method to have no
zero-information strategy; so why not at least achieve that?
This version of IRV-completed Condorcet of yours,
(with your step 2) has a big and obvious random-fill incentive. Voters who are sincerely indifferent regarding their lower1. Eliminate non-members of the minimal dominant set. 2. Eliminate all candidates who are pairwise-beaten by a full majority UNLESS this doesn't leave anyone at all. 3. Hold an IRV tally between remaining candidates.
choices should (at least) random-fill, because they might give one of their favourites's opponents a "majority defeat" that
that candidate might not otherwise have (which, if their favourite has one, might save their favourite from being eliminated).
(I suppose there is a small chance that it could backfire, by causing the elimination of a candidate that otherwise would have
lost to Favourite in the final runoff.)
To me it is just obviously unfair that insincere random-fillers should have more voting power than sincere truncators.
If the method used is something like IRV or Margins, and the voters assured (by election officials and all the media pundits)
that without taking into account how others might vote the do best to just vote their full sincere preferences, then I think most
(or many) voters will just respond "that's fine" and do just that.
If on the other hand, they are told that they would be mugs to not give a full strict ordering regardless, then I think that some
of these voters would think "I don't want to vote randomly, and I don't think the result should be determined by people
voting randomly. If , with 'zero-information' I can do better by random-filling, then maybe I can make use of some information
to do better still for my favourite." And so they are encouraged down the path to outright order-reversal.
So to sum up the main effects of your step 2: naive sincere truncators will be unfairly disadvantaged, and if the voters are
savvy then the result will tend to be randomized and there will be more Burying strategising.
I don't see why Condorcet, Truncation Resistance, Minimal Defense should be incompatible with No Zero-Information
Strategy. As far as I can tell, they are all met by Schwartz // SC-WMA that I described in the "recommendations" thread
in September this year.
CB: I am astonished that you are not bothered by failures of mono-add-plump and mono-append. These criteriaMy answer to your second question is "No". I assume we all agree that two completely essential criteria that a method must meet are Woodall's "Mono-add-plump" and "Mono-append".Er, "completely essential"? "must meet"? "all agree"??? I don't know about that assumption, Chris...using IRV (aka AV) to complete Condorcet by eliminating and then ignoring the not-allowed-to-win candidates not in the "top tier" creates a method that fails both Mono-add-plump and Mono-append.abcd 10 bcda 6 c 2 dcab 5 All the candidates are in the top tier, and the AV winner is a. But if you add two extra ballots that plump for a, or append a to the two c ballots, then the CNTT becomes {a,b,c}, and if you delete d from all the ballots before applying AV then c wins.My question is whether it is likely that voters will frequently be able to exploit this strategically, and whether their efforts to exploit it are likely to seriously distort their reported preference rankings. If not, then I suggest that the problem is not very severe.
are very easy to meet (much more than mono-raise, aka regular Monotonicity) and to me their failures are completely
absurd . You must at least agree that it is a huge potential marketing problem in the face of detractors.
CB: I think that would open the door to IIA-like absurdity. Say, in a race between a,b,c,d, a wins and d is ignoredCB: In his example, in both the "before" and "after" cases all the candidates have a "full majority" pairwise loss. (You don't spell it out, but I assume "full majority" means more than half those ballots that distinguish between any of the Schwartz-set members.)I was just thinking more than half of the valid vote, to keep things simple.
by all the voters. Then two or three extra ballots are found and admitted, and they vote for d and ignore abc. This changes
the winner from a to b .
Regarding Woodall's "CNTT, AV" (Condorcet (Net) Top Tier, Alternative Vote) I forgot a small detail.
(BTW, the Condorcet (net) top tier is another name for the Smith set; and the Alternative Vote is another name for IRV).
Woodall writes that if none of the CNTT candidates have any first-preferences, "then this is equivalent to choosing one at
random (not necessarily with equal probability). If this is considered unsatisfactory, then one should first exclude all the candidates
in the Condorcet bottom tier, and repeat until some candidate in.. [CNTT].. has a first-preference vote, before applying AV as
above."
Chris Benham
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