# Presidential 2-method vote

Sun Nov 24 22:45:40 PST 1996

```Mike challenged Don to the following test:

> How about we have a rank-balloting election for President, and we'll count
the ballots in 2 ways: Condorcet's method, & IRO. Then, we'll hold a 2nd
balloting, between the winner by Condorcet's
method & the winner by IRO. In other words, we'll let the people choose
which winner is the President that they want.
You don't object to letting the people choose, do you? Guess which one would
win :-)
Mike

Mike, it might be rash to challenge Donald to this particular contest since,
with Smith-Condorcet or "plain Condorcet" as you and Steve have defined it,
there's no guarantee that Candidate C who wins under Condorcet will
necessary beat Candidate IR who wins under Instant Runoff. That is, if there
is no Beats_All winner, and the "default Condorcet winner" is the one who
has the smallest negative vote against her, then C could well win under
Condorcet because IR polls "only" 55 votes against C's 45 in the IR-C
contest, 55 being the smallest maximum defeat. Whereas if it just so happens
that the final count under IRO - the "tour decisif", to use the French term
- saw IR pitted against C, then IR  would win with 55 votes to C's 45. Thus,
the IRO winner would _also_ beat the Condorcet winner pairwise, even in a
"straight fight" between those two candidates only.

I do agree with you and Steve that Condorcet is superior. Condorcet counts
the "number" of two-way victories, after all combinations of candidates have
been considered - not "number" in the crude and manipulable sense of
Copeland's method, but in that once a candidate reaches the magic number of
[total candidates minus one] pairwise victories, she is guaranteed of
election. (Eg, if out of five candidates, one has four pairwise wins, she'll
be the "absolute Condorcet winner" or, as Steve prefers to call it, the
Beats_All candidate.) Whereas IRO focuses on one single pairwise contest
only, and determines which will be the "decisive" contest through the
lottery of low-man-out elimination.

I do agree that Condorcet is better than IRO by various criteria
(particularly monotonicity and non-manipulability), but this particular one
above isn't one of them, or at least not reliably so.

Tom

-------------------
Overflow-Cc: 100245.2440 at compuserve.com ('Geoff Powell'),
bmusidla at email.dot.gov.au ('Bogey M'),
c-p-r at netcom.com ('Citizens for Proportional Representation'),
crabb.deane at pi.sa.gov.au ('Deane Crabb'),
dunnmj at ozemail.com.au ('Martin Dunn'),
election-methods-list at eskimo.com ('Election methods'),
GGoode at VTRLMEL1.TRL.OZ.AU (Goode, Geoff),
j.pyke at qut.edu.au (John Pyke, QUT Law School),
jhtaplin at cygnus.uwa.edu.au ('John Taplin'),
lee at cs.mu.OZ.AU ('Lee Naish'),
martinw at cse.unsw.edu.au ('Martin Willis'),
mdt at ozemail.com.au ('Matthew Townsend'),
voting-systems at netcom.com ('Voting-systems')

```