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

[Kristofer Munsterhjelm]

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.