[EM] Re: Condorcet completed by IRV

[Chris Benham]

James G-A,
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.

>(from Steve Eppley's MAM site)
>
>  
>
CB: To answer your question,  I  think that the Truncation Resistance 
criterion (as defined above)  is  desirable but not
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,

>1. 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.
>
(with your step 2)  has a big and obvious random-fill incentive. Voters 
who are sincerely indifferent  regarding their lower
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.

>My 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.
>
>  
>
CB: I  am astonished that you are not bothered by  failures of   
mono-add-plump and mono-append. These criteria
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: 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.
>  
>
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 ignored
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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