[EM] election-methods Digest, Vol 26, Issue 14

[Warren Smith]

>In your example of 3 main rival candidates (A, B, C) and one dark horse
candidate (D), you said that range voting prevented the dark horse from
winning. Graphically speaking, there would be a triangle formed by the
three main candidates , while the dark horse would lie somewhere outside
of it.

>My question is, what if the dark horse candidate is in fact a compromise
candidate (i.e. his position D is inside the triangle formed by ABC)? In
this case, he might truly be second choice on all the ballots without
being first choice on any of them.

Michael Rouse
mrouse1 at mrouse.com

--REPLY by WDS
In a situation where ABC are the vertices of an equilateral tirangle, D is its center,
and all voters are located at ABC and prefer candidates closer to them, then
yes, each voter honestly would rank D 2nd and D would then be the honest Condorcet winner.
D might also be the honest range voting winner (depends how the honest voters score
people) or it might be one of {A,B,C}.

In this situation the C-voters in Condorcet would be motivated to strategically downgrade
D in their votes to bottom below all others.  If enough voters did that D would
no longer be Condorcet winner and one of {A,B,C} would win.   Of course in that case
some voters who lost would want to upgrade D...   

In range voting, the C-voters also would like to vote C=99, B=A=D=0 and if enough
voters acted that way one of {A,B,C} would win; but then the voters for the losers
would be motivated to upgrade D to 99 co-equal top, and then D would win.

...so... I don't think Rouse's scenario leads to any clear victory fo range over
Condorcet or vice versa  (I think it was intended to make Condorcet look
superior to Range, but that isn't happening).

wds