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

Steve Eppley seppley at alumni.caltech.edu
Thu Aug 8 14:26:41 PDT 1996

```Hugh T wrote:
-snip-
>I had thought it was agreed that a voter ranking candidates
>equally should at least have the option to cast half-votes each way,

No, I don't agree.  It's something I considered for awhile, but
eventually I concluded that what ought to be measured, in order to
pick the candidate who maximizes consensus (i.e., minimize the
number who oppose), is the number of voters who prefer the
pair-opponent more than the candidate.  (If I extend the analogy of
the Consensus system, counting don't_care as 1/2 vote for and 1/2
vote against would defeat every proposal and not really measure the
number of voters who oppose.)

With the "correct" measure, it doesn't matter in the AB pairing
that the C>A=B voter will be unhappy if A or B beats C; that
unhappiness is properly counted only in the AC and BC pairings.

Counting the number of voters who will be unhappier if the result
changes is different from measuring the amount of unhappiness.

1:  C > A > B
1:  C > B > A
98:  A=B
Here one person will be unhappier if the winner changes from A to B.

2:  C > A=B
98:  A=B
Here no one will be unhappier if the winner changes from A to B.
You want to make it easy for the 2 to tactically combine their
ballots to maximize their effectiveness.  I feel no obligation to
make this easy, and see it as a "cure" which is worse than the
"disease."

-snip-
>That only 46% voted against a candidate in her only loss is more
>impressive if the reason is that a large number of voters ranked her
>equally with another at the top of their ballots (or at least above
>all other members of the Smith set), than it is if a large number
>ranked her equally with another at the bottom of their ballots. In
>the former case it could be that electing either A or B would
>maximize the political utility of the voters who ranked C last, so
>46% really reflects the total "unhappiness" from the election of A.
>In the latter case it seems that 46% understates aggregate
>unhappiness.  In that case I do not see that we should measure
>aggregate unhappiness as being less than it would be if the "C"
>voters who ranked A and B equally had instead split equally between
>them.

I don't think we can or should try to measure "aggregate"
unhappiness.  When I wrote about what Condorcet(0) is measuring,
maybe I wasn't clear.  I'm talking about measuring a "relative"
unhappiness: whether the voter would be happier or unhappier if
A is elected instead of B, which has nothing to do with C.

-snip-
>>>28 Dole, Clinton
>>>20 Clinton
-snip-
>>A question we shouldn't ignore about the alternative scenario is:
>>who *ought* to win with those sincere preferences?  Why not Nader?
>>If the win is instead accorded to Clinton, 48 voters will be
>>happier and 52 will be unhappier.  If the win is accorded to Dole,
>>46 voters will be happier and 54 will be unhappier.
>
>If Nader wins because the Clinton voters could have elected
>half-votes but ignorantly voted only for Clinton in the belief that
>a second ranking would be used only to decide between Dole and Nader
>(whom they find equally unacceptable), then I count this as a failure
>of an unduly complex system.

I wouldn't call it a failure unless there's a good reason why Clinton
makes a better winner than Nader here.

>If Nader wins because the Clinton voters did not even have the
>prevail in the case where he is ranked equally with Dole at the
>bottom of all Clinton voters' ballots, when had the Clinton voters
>all voted a second choice, and two-thirds of them had actually
>Clinton voters be coerced into voting false preferences in order to
>maximize the chance to elect their candidate?

I don't think you've answered my question: why is it wrong for Nader
to win with these *sincere* preferences?  (If 2/3 of the Clinton
that's a different set of preferences.)  Clinton isn't a "middle"
compromise here, and we don't need to design the method to elect
him in this scenario.

The "coercion" you mention isn't a problem as serious as the LOE
dilemma, since the voters aren't "forced" to rank a less-preferred
choice as high or higher than their true favorites.

Perhaps we should see what happens if wing voters are given the
opportunity to tactically vote 1/2 against middle & opposite wing.
It may be "good" for society when the middle voters are allowed to
have been about the middle case--but does it still work out as well
when the wings can use it too?

46:  D          <--  1/2 votes against both in the CN pairing?
20:  C          <--  1/2 votes against both in the DN pairing?
34:  N>C>D

D<C  46<54                             D<C  46<54
C<N  20<34                             C<N  43<57
N<D  34<46                             N<D  44<56
C's largest loss is smallest.          D's largest loss is smallest.
If the 46 are tactically trunc-        If the 46 are tactically trunc-
ating D>C>N, they've failed.           ating D>C>N, they've succeeded.
The N voters have a LOE dilemma.

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

```