[EM] Winning-votes intuitive?

[Adam Tarr]

Rob wrote:

>I think the reason the winning-votes method seems more intuitive in this 
>case is that, looking at the votes, there seem to be 49 Bush voters and 51 
>Gore/Nader voters, so a Bush result seems wrong.  But that's 
>misleading.  The 24 Gore voters don't prefer Nader to Bush.  If they had 
>voted Gore>Nader>Bush, then I'd agree that Bush should lose.

Ah, but that's not the problem.  I tried to make the example as simple as 
possible, but I can add the full and natural Gore voter preferences with no 
effect.

49: Bush
12: Gore, Bush
12: Gore, Nader
27: Nader,Gore

Bush beats Nader 61-39
Nader beats Gore 27-24
Gore beats Bush 51-49

Ranked pairs still gives the election to the (now more explicit) Bush 
minority.  SSD still gives it to Gore.  I don't think the 51-49 divide in 
Gore and Bush supporters is at all misleading.  It is the expressed 
preference of the voters.

>But, if you ask me, the above election
>is more accurately expressed as
>
>49:Bush>Gore=Nader
>24:Gore>Bush=Nader
>27:Nader>Gore>Bush
>
>which should be equivalent to
>
>49:Bush>Gore>Nader
>49:Bush>Nader>Gore
>24:Gore>Bush>Nader
>24:Gore>Nader>Bush
>54:Nader>Gore>Bush

I picked real names, in stead of A,B,C, in an effort to diffuse this sort 
of convoluted argument.  In order to give the election fairly to Bush using 
SSD, you need to give half the Bush voters a second preference of 
Nader.  This hardly seems like their actual preference.  Why not simply 
accept that they truncated their ballots because it made sense to in Ranked 
Pairs?  They have nothing to fear from Nader, since they can tell coming 
into the polls that the Bush-Nader margin is by far the largest of the 
three.  Nader is the only candidate who can't win, as it should be.  (Did I 
mention that in my first example, Nader wins with Black or other Borda 
methods?  That's a straw man, since rational voters would not vote like 
that in Black, but still...)

This is a totally reasonable strategic truncation on the part of the Bush 
camp.  They have nothing to lose, since Nader is a sure loser anyway, and 
the election to gain.  If these people vote Gore second (which is their 
obvious second choice) then all they do is make Gore the Condorcet winner 
and hand him the election.  Why would they do this?  Moreover, it is not a 
tough sell to make Bush voters leave off a second preference; most of them 
probably don't like the idea of voting for Gore anyway.

The only way the Gore-Nader camp can prevent this is by convincing some 
Nader supporters to rank Gore first, or for twice as many to rank Gore 
equal with Nader.  This is classic favorite betrayal/lesser of two evils 
stuff.  A much harder sell.

>  if I were one of the Nader voters (*shudder*) and a winning-votes method 
> were being used, I'd vote Nader=Gore>Bush.  Winning-votes methods may 
> discourage truncation, which is nothing more then tied rankings at the 
> bottom, but they strongly encourage tied rankings at the top.

Why would you do so here?  In SSD, As a Nader supporter, in this example, 
you would say, "Well, Nader's got no shot, it just comes down to 
Gore-Bush."  And you could vote Nader>Gore with virtually no fear that you 
damaged your chances of getting a favorable outcome.  On the other hand, 
with a margins method, I've already shown how the tied top rankings you 
suggest would be a necessary defensive strategy.

The only way the Bush voters can win with their minority in SSD is if they 
convince almost exactly half (but not many more, mind you) of their voters 
to vote Bush>Nader.  Not only is this highly non-intuitive for the Bush 
voters, but it is risky, since if they overdo it they could hand the 
election to Nader!  Furthermore, if the Bush camp tries to co-ordinate this 
sort of massive manipulation scheme, the Nader camp will get wind of it, 
and they could block it easily by having a small portion of their voters 
switch over to Nader=Gore.  Then, and only then, is the defensive strategy 
you suggest for them needed.

>   In fact, I'd vote ties in the top half or so of my ballot, even if I 
> had *zero* information about the other voters' preferences!  "Margins" 
> methods don't encourage tied rankings like that on average, although of 
> course there will be situations that reward insincere voting in any method.

I guess it goes without saying that I have missed the rationale for voting 
tied leaders in SSD and not in margins.  I see a clear motivation for doing 
the opposite, however.  Could you provide some fairly simple/reasonable 
examples that illustrate it?  I consider the example I gave to be a 
reasonable one.  I came up with it before I was aware of the 
margins/winning votes debate, and in fact, before I was even aware of the 
difference between Ranked Pairs and SSD.

-Adam