# Tobin-Condorcet bad example? (was Re: Election Methods Poll (fin

Steve Eppley seppley at alumni.caltech.edu
Wed Oct 2 01:02:24 PDT 1996

```Hugh T wrote:
> "In each pairwise contest between X and Y, count as 1/2 vote for X
> and 1/2 vote for Y an equal ranking of X with Y by a voter, if that
> voter ranked all other members of the Smith set ahead of X and Y.
> Otherwise count the ranking as 0 votes for each."
-snip-
>When I made the proposal I thought it intuitively obvious that
>counting equal rankings for tiebreak purposes in a manner that
>would better reflect the preferences of the sincere voter in case
>of a circular tie, without giving that voter more voting power
>than is consistent with one-person-one-vote, would be desirable
>on democratic principles.

Some time ago I pointed out that Hugh's examples which make his
variant appear rosy illustrate scenarios where the middle candidate's
consider what happens when a wing candidate's supporters take

Suppose three candidates Right, Middle, and Left are running and
100 voters cast these ballots:

46:  R
20:  M
34:  L > M > R

The pair matrix:

R    M    L
R         46   56L
M    54L       43
L    44   57L
---- ---- ----
LL:  54   57   56

(Notes:  The number in each matrix cell is the number of voters who
prefer the row candidate more than the column candidate.  The L
suffix indicates a pairloss of the column candidate.  The LL row
shows the largest loss in the column.)

If I haven't made any arithmetic errors R is the winner here,
since the smallest largest_loss (54) is his.  If the half-votes
aren't tallied, M is the winner:

R    M    L
R         46   46L
M    54L       20
L    34   34L
---- ---- ----
LL:  54   34   46

I consider this to be a "bad example" of Condorcet(1/2), since
it shows how wing voters can steal an election from the sincere
beats-all winner by misrepresenting their R>M>L preferences.
This possibility presents a dilemma for the other voters, since
they may want to misrepresent their own preferences (L=M>R) to
guard against it.

For me, this is a violation of important democratic principles.
Picking the optimal winner when there's a sincere circular tie is
somewhat less important than picking the sincere beats-all winner
when there is one.  And incentives to misrepresent preferences muck
up the mandate and the perceptions of where the people stand.

Even if the ballots in this example are sincere, the case for
electing Middle appears stronger than the case for electing Right.
We've discussed this many times: the majority who prefer Middle
more than Right, etc.

Also, I don't think it's a correct heuristic that it's in a group's
best interest to let each member of the group do whatever s/he
wants.  I agree with Mike that the 1/2 votes are phantasms of
the quantity that we want "votes against" to measure so it can
be minimized: "the number of voters who would be bothered if the
pairloser were elected instead of the pairwinner".  The equal-
ranking voters wouldn't be half-bothered; they'd be indifferent.
Giving voters the power to claim they'd be half-bothered is not
in the group's best interest.

By the way, Hugh, would you prefer that I change the report so the
name of the method is Tobin-Condorcet?  I will if you don't object.

---Steve     (Steve Eppley    seppley at alumni.caltech.edu)

```