# Consensus, Condorcet(0), and Condorcet(1/2)

Hugh R. Tobin htobin at ccom.net
Fri Jul 26 07:34:41 PDT 1996

```At 01:04 PM 7/25/96 -0700, Steve Eppley wrote::
>[A message I sent to EM was eaten when eskimo.com broke down last
>week.  Here's the gist of it, hastily rewritten.]
>
>methods led me to think about what it is that the method ought to be
>measuring, and ponder the following question:
>
>Which of the following is the greater violation of democratic
>principle in a 2-candidate race:
>
>1. Electing candidate A even though A lost to B (46 to 54).
>2. Electing candidate A even though A lost to B (34 to 46,
>     with 20 who have no preference between them).
>
>There's no clearcut answer, seems to me.  In case 1, A has a smaller
>margin of defeat and more supporters than in case 2.  But in case 2
>there are fewer voters who would be made unhappier by changing the
>result from B to A than in case 1.
>
>Condorcet(0) implements the principle that case 1 would be a greater
>violation of democracy.  It tries to minimize the number of squawking
>voters when breaking the circular tie.  I don't know what Condorcet(1/2)
>implements.
>
>>---Steve     (Steve Eppley    seppley at alumni.caltech.edu)
>

But in the tiebreak we are comparing the results of at least three pairwise
races.
The voter who ranked C higher than both A and B is clearly unhappy with
A's victory.  The question is whether it is fair or democratic that if C beat B
by 60-40 but lost to A 51-49,  A should win over C under your case 2 because
a large
block of the C voters considered A and B equally detestable, whereas if the same
block were split evenly between A and B (or engaged in vote-pairing to express
their indifference in the manner most favorable to C), their own candidate
would win.
Giving the victory to C in that case, by counting A as having 56 against,
seems more democratic
because it gives effect to the unhappiness of the C voters with A, without
giving them
any extra "votes-against" for tiebreak purposes due to their equal ranking
of A and B
(as in one odd variant mentioned recently as a straw man, where one could
cast a whole
vote against  each).  Where voters rank  candidates equally at the bottom of
their ballots,
counting one-half each way more truly captures the hypothetical unhappiness
of those voters.
The "zero" rule could be said to falsify their preferences by treating them
objection to either A or B.

Where the equal rankings are at the top of a ballot, one might argue that
the voter would be totally
satisfied with either one and thus should not be forced to cast a half-vote
against each, with
the possible result of victory for her lowest-ranked candidate in case of a
circular tie.
Hence my modest proposal, posted earlier, which also reduces the pressure on
the C voter
to falsify a preference between A and B merely so as not to lose one of her
alloted