[EM] NESD and NESD* properties of a single-winner voting method

[Jonathan Lundell]

On Nov 10, 2009, at 5:07 AM, Kristofer Munsterhjelm wrote:

> Jobst Heitzig wrote:
>> Dear Warren,
>> I don't seem to understand the definition:
>>> A single-winner voting system "fails the NESD property" if, when every
>>> honest voter
>>> changes their vote to rank A top and B bottom (or B top and A bottom;
>>> depends on the voter which way she goes), leaving it otherwise
>>> unaltered, that always (except in very rare "exact tie" situations)
>>> causes A or B to win.
>> So, when all voters vote strategic (i.e. no voter is honest) and all
>> leave their ballots unchanged, then by definition "every honest voter
>> changes their vote to rank A top and B bottom" but of course no system
>> changes the result since no ballot is changed. Hence no system fails NESD.
>> What is the misunderstanding here?
> 
> I think he means:
> 
> Call the first group of ballots, X, consisting of ranked ballots made by honest voters. Now take every ballot in X and, for each ballot y, if y votes A > B, put A first and B last, or if y votes B > A, put B first and A last, leavin the ballot otherwise unchanged. Call the modified bundle, consisting of these modified y-ballots, X'.
> 
> If there exists such a group of ballots X so that the method in question gives a different victor when fed X and when fed X', and gives either A or B as the victor for group X', then it fails the NESD property.
> 
> In other words: if the entire electorate decides that the dangerous contest is A vs B and so maximally buries the one they like the least, and this strategy pays off, then it fails this property.

That's the way I read it. In other words, interpret Majority failure as a virtue.