[Election-Methods] RE : Corrected "strategy inCondorcet" section

[Abd ul-Rahman Lomax]

At 12:41 PM 8/17/2007, Dave Ketchum wrote:
>Paul's words are tempting, for this exchange has little to do with
>desirability of Condorcet, or of margins vs WV.

That is true.


>Looking closer, the votes are:
>       1000 A>B>C=D
>       1000 C>D>A=B
>          1 D>B>A=C
>
>2000 voters rate A vs C as a tie, only agreed that B and D should lose.
>
>The one vote agrees to the A vs C tie, but mostly muddies the water.

That also is true.


>So, a not believable election tally gets debated for weeks.

Dave is on a streak....

The example is one where most methods would assert a tie. Range might 
not, but we cannot predict how these voters would vote in Range, nor 
in Approval. However, there is one fairly easy assumption about 
Approval: you would not see any significant number of triple 
approvals. But how many bullet votes you would see, I don't know. If 
the truncation indicates some significant preference gap, we could get

       1000 A, B
       1000 C, D
          1 D, B

In which case it is a tie between B and D.

One serious flaw in the study of elections through specific scenarios 
is that they neglect completely, sometimes, the extreme rarity of the 
scenario being studied. This scenario requires a thousand voters in 
two camps to all vote identically, exactly, no exceptions.

Now there is one way to understand this election. Suppose it is 
Approval+PW, as I have more recently defined it. And there are only 
two voters, each with 1000 votes to cast, i.e., it is Range 1000.

Even if these are individual voters, it is quite realistic to presume 
that, since they vote so identically, they would naturally form a 
party which can internally generate consensus. Or party discipline 
can enforce it, our studies of election methods frequently disregard 
such details, such as whether or not secret ballot is being used.

So, looking at this as two voters only, they have voted in Range 1000:

1: A 1000+, B 1000, C 0,     D 1,    and
2: A, 0,    B 1,    C 1000+, D 1000

(I have assumed something that I've proposed, which is that it is 
possible, on the ballot, to express a preference that does not affect 
the rating, I generally call this Plus. A+, then, uses and Approval 
ballot and a Plus indicator (which is also overvotable, but I suspect 
that few would use it that way). How the Plus indicator is used is a 
separate question.)

This is actually quite a reasonable scenario, excepting only the 
rarity of such exact ties. A and B candidates are affiliated with the 
first party, and C and D with the second, but the two camps wanted to 
indicate, with their votes, a very small preference for one candidate 
from the opposing camp. If there is a spectrum here, B and D are 
toward the center. Not enough, however, to cause party members from 
the far end of the spectrum to drop their ratings (this is not 
particularly believable), since they *did* drop the ranking, they did 
not top-rank equal, and they *all* had the same internal ranking.

And with this understanding of the votes, which *could* be an 
expression of utilities that would explain the votes, we can see that 
it really is a two way tie, in Range analysis, and a two-way tie in 
preference analysis, with the two winners being equal. Preference 
analyis strongly indicates that the pairwise election, the tie that 
must be resolved, is between A and B, by a large margin. Range 
analysis indicates, however, that a runoff would be between C and D, 
since they each got a slightly higher total score, due to the vary 
small rating preference expressed.

In Range with pairwise-detected runoff, which I've recommended, there 
are two Range winners, and two preference winners who beat both of 
the Range winner. In real elections, this would be extraordinarily 
rare. Now, this scenario represents, really, two distinct parties. I 
expressed that with two voters. How would these voters resolve the question?

The scenario shows, ultimately, the shortcomings of election methods 
in general, they should be considered devices of convenience only, 
never to be considered superior -- except in efficiency under some 
conditions -- to deliberation and negotiation. These two parties 
seriously need to work it out together, or agree to toss a coin, and 
perhaps toss coins more than once....