Example with contrary half preference votes

[Hugh R. Tobin]

Steve Eppley wrote:
> 
> Hugh T wrote:
> -snip-
> >Consider a slight modification of this scenario: Dole's strategists
> >get a minority of his supporters, 18 per cent of the total, to
> >order-reverse (alternatively, they really prefer Nader), the rest
> >sincerely vote Dole, Clinton.
> >  28 Dole, Clinton
> >  18 Dole, Nader
> >  20 Clinton
> >  34 Nader, Clinton
> -snip-
> >No rational Clinton voter who understood the system would refrain
> >from choosing the 1/2 vote option,
> 
> Can the Clinton voters reliably predict that only 18% will order-
> reverse (or really prefer Nader to Clinton)?  Wouldn't they be afraid
> that a few more clever Dole voters would also reverse, electing Dole
> by increasing the size of Clinton's largest loss (to Nader)?
> 
> The only ways to defend against that would be to try to make Dole's
> largest loss larger than Clinton's (by persuading Nader voters to
> vote C>=N) or by keeping Nader from losing badly to Dole (electing
> Nader and "punishing" the reversers by voting N>D or by *not*
> choosing the 1/2 option).
> 
> It looks like all the voters would have a strategy dilemma in this
> example, with such precise knowledge of a close circular tie.
> 
> -snip-
> >Perhaps the voter should have to give a rational explanation of why
> >he would not want the 1/2 vote to count in case of a tiebreak, in
> >order to opt out of it.
> 
> Besides making voting more complicated and daunting, it raises the
> question of who gets to judge whether explanations are rational.
> 
> ---Steve     (Steve Eppley    seppley at alumni.caltech.edu)

My last suggestion was meant to be facetious, but also to make the point 
that half-votes should be the default option, so that a voter who simply 
votes for his own candidate, sincerely registering his indifference among 
the others, will not have omitted to do everything he sincerely can do to 
elect his first choice, merely because he does not understand the 
subtleties of the tiebreak, which have puzzled even some on this list.

The criticism of my example seems to assume that the Clinton voters have 
some interest in electing Nader in preference to Dole, when by hypothesis 
they are indifferent between those two.  

I do not think my example is too implausible: it assumed either (a) what 
has been suggested on this list -- that order-reversal on a scale 
sufficient to swing the election (make Dole less beaten than Clinton) 
would fall short of success (perhaps even because of an announced 
deterrent); or (b) that the there was a sincere split in second choices 
of Dole voters. 
 
Of course the Clinton voter cannot reliably predict the other votes when 
he goes into the booth.  But that is a good reason why he would 
rationally choose the 1/2 option -- it might make Clinton win, as in my 
example, and it certainly cannot hurt Clinton's chances.  The voter does 
know that how he casts his vote will have no effect on the other votes -- 
any deterrent value would have to be for the next election.  I suggest 
this is a very attenuated rationality for choosing the "zero" option in 
order to assure the election of Nader (by hypothesis, no better than 
Dole), when there is a chance that choosing the one-half option will 
result in electing Clinton.

Of course, if there is no announced order-reversal strategy by Dole -- if 
the circular tie is "natural" -- then choosing the zero option lacks even 
the strained "rationality of irrationality" (carrying out the threat 
after deterrence has failed).  

If selecting the zero option is a conscious strategy, the voter will be 
prepared to check a box (or the equivalent).  I think that box should 
have a warning label, something like: "Checking here cannot improve the 
chances for your most favored candidate to win.  Checking here may result 
in the defeat of your higher-ranked candidate by a candidate that you 
have ranked equal to a lower-ranked candidate, or that you have not 
ranked at all."

I believe Ossipoff's first example, where all Dole voters insincerely 
truncate without choosing the 1/2 option, is the less plausible one, for 
reasons he has suggested -- if they want to manipulate the system, 
truncation is a weak method.  I infer from their votes that they really 
are indifferent between Clinton and Nader.  That means there is no 
Condorcet winner, and we should not count the system a failure if Clinton 
loses.  But if Clinton wins because people do not understand the 
relationship between the half-vote option and the chances of electing a 
candidate that they rank above those to whom they would give the 
half-votes, I do count this as a failure.  The Dole voters may sincerely 
feels "there is no way I would cast even half a vote for either Clinton 
or Nader against anyone".
    
I think the rule I proposed will faithfully register the intent of 
truncation or equal ranking in the overwhelming majority of cases, and I 
think if the only reason that can be advanced why one would choose the 
zero option is the "truncation to deter order-reversal" strategy, then 
making the 1/2 option automatic may gain more in simplicity than it loses 
in offering meaningful voter choice.  But I would settle for making 1/2 
the default option, with a suitable warning.  After all, this is all a 
very minor quibble about a detail of the system.

-- Hugh Tobin