# [EM] (CIRCLE) Cardinal [I] Rating Condorcet Loser Elimination

Dgamble997 at aol.com Dgamble997 at aol.com
Wed Sep 3 15:12:03 PDT 2003

```Donald and list

The Condorcet v IRV debate on the EM list increasingly reminds me of the a
description of debates in the Stormont ( Northern Ireland ) assembly between
Unionists and Republicans- " not so much a debating chamber more a gladiatorial
arena for the restatement of entrenched positions ".

In my original post I wrote:

David: "Actually neither myself nor those who disagree with me can be
certain as to whether B is really a low utility turkey ( the least worst)
or a popular compromise (the most best). This is because ranked ballots
just tell us that the first choice is preferred to the second choice not
how much the first choice is preferred to the second choice."

You replied:

Donald: Only the voters (all of them) can answer those questions and only
the voters should be allowed to answer those questions.

The idea was to give the voters a ballot on which they could indicate their
utilities and  a method that would take them into account in deciding the
winner.

Donald also wrote:

"Donald: How often will your method, `Cardinal [Insidejob] Rating Condorcet
Loser Elimination' (CIRCLE), elect the ESBS-winner, the standard for all
single-seat methods?"

I will stick my neck out here ( knowing the likelihood of  my decapitation )
and say that I think CRCLE will perform quite well against this standard.

Take the simplified example:

49 A>B
3B
48 C>B

For B to win in this situation she/he must have a minimum utility of 0.92 to
A>B voters and a minimum utility of 0.96 to C>B voters. To win B has to be
highly liked (approved?) by everybody.

49 A1.00 > B0.92
3 B1.00
48 C1.00 > B0.96

A versus B     49 v 49.08  B wins
A versus C     49 v 48      A wins
B versus C     48.08 v 48  B wins

C is the Condorcet loser and is eliminated.

C's votes transfer to B at a value of 1.00.

B (51) wins against A (49).

If debate where allowed between the ESBS voting rounds the voters/ candidates
may well realise that everybody rates B highly and elect him/her.

In the example:

39 A1.00 > B0.30
14 B1.00 > A0.50
9 B1.00 > C 0.50
38 C1.00 > B0.25

B has only 30 % of the utility of A to A > B voters and 25% of the utility of
C to C > B voters -not liked by either group of voters much, not really any
kind of acceptable compromise.

A versus B    39 v 32.5  A wins
A versus C    46 v 42.5  A wins
B versus C    34.7 v 38  C wins

B is the Condorcet loser and is eliminated.

B votes transfer 14 to A and 9 to C at a value of 1.00.

A (53) wins against C (47).

Again if debate were allowed between the ESBS rounds of voting A  and C
voters would realise they didn't think much of B, B voters would realise this too
and B would either withdraw or lose support until A finally won.

David Gamble

Exhaustive Secret Ballots Standard (ESBS): by Donald Davison

* One secret vote per person.
* If one candidate has a majority on the first ballot, that candidate
wins - election is over.
* If no candidate has a majority, then there will be a next ballot, etc,
until there is a candidate with a majority.
* No candidates are eliminated, but a candidate is allowed to withdraw
after any ballot.
* No voter is forced to change his vote, but any voter is allowed to
change his vote on the next ballot.

* The final winner will be the result of the actions taken by the
candidates and the voters.
* Whoever is the winner of the ESBS election is the correct winner.
* While we would not use Exhaustive Ballot for an election, any method
that is used must be compared to ESBS, that is, does the method elect the
ESBS-winner?

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