[EM] Condorcet How?

[Juho]

On Apr 8, 2010, at 3:29 AM, robert bristow-johnson wrote:

> On Apr 7, 2010, at 6:25 PM, Dave Ketchum wrote:
>
>> This is some thought about keeping it simple, yet doable.
>>
>> I will lean toward Ranked Pairs with margins,
>
> not sure what "with margins" does.

There are different approaches to determining the strength of the  
pairwise comparisons.

Let's say that there are 100 voters. 40 voters prefer A to B. 35  
voters prefer B to A. The remaining 25 have not indicated any  
preference between A and B.

The most common ways to measure how strongly the voters preferred A  
over B are margins and winning votes. In this example the margin of  
this comparison is 5 (40-35). Winning votes counts the votes that  
preferred the winner (A) over the loser (B). In this example the  
strength of B's defeat to A is 40. A's defeat strength (to B) is  
considered to be 0 since A won.

Depending on which approach a Condorced method uses the winner may  
change. These two approaches differ only if some voters do not  
indicate any preference between A and B. For example margins considers  
victory 45 against 10 to be stronger than 49 against 48, but winning  
votes considers the latter opinion to be stronger.

There are also other approaches like counting the opposing votes  
(without considering which one of the candidates wins). Or one could  
for example make the margins proportional to the number of voters that  
had an opinion => (40-35)/(40+35) or maybe 40/(40+35). But margins and  
winning votes are the ones that are most commonly used.

> i think that it's likely that in the worst case of a goddamn cycle,  
> that probably Markus's method would better reflect the will of the  
> voters than Tideman, but the two don't disagree with a cycle of 3 in  
> the Smith set, and i think that if either were adopted, it would be  
> a few millennia before there would be a Condorcet-decided election  
> that would be decided differently between Tideman and Schulze.

Yes, it could take a really long time before we would get a top level  
cycle with four or more members and where these two methods would give  
different winner, assuming that all candidates are ranked in all  
votes. We could however get much sooner a difference between a method  
that uses margins and a method that uses winning votes. The number of  
voters that do not take position on all pairwise comparisons may vary  
a lot between different pairwise comparisons. People may e.g. not rank  
the candidates of the competing wing/party. And if there are many  
candidates that are about equal in strength margins and winning votes  
could quite well elect a different winner.

There are also different ways to solve the cycles. The Tideman and  
Schulze methods use both the approach of overruling some of the  
smallest expressed pairwise opinions, creating a linear social  
preference order, and they use chains of victories to determine the  
strength of each candidate. Some other methods like minmax base the  
decision solely on how each candidate relates pairwise to other  
candidates (at one step, i.e. paths of defeats are not considered).  
One key reason behind these various approaches to solving circular  
preferences is the interest to develop methods that are immune to  
clones. In practice this means interest not to punish or reward  
parties/wings if they nominate multiple candidates. Condorcet doesn't  
have problems with clones when there are no cycles. And clone problems  
in the presence of cycles may also be quite rare. But nevertheless,  
different approaches to solve these problems have been proposed.

Just to mention one clone risk elimination approach that differs from  
the approach in the above mentioned two methods, one could explicitly  
indicate which candidates are considered to be clones. One could let  
the nominated candidates to be grouped so that they form a tree-like  
hierarchy. Defeats to candidates in another branch would be considered  
stronger than defeats within one branch. The simplest approach is to  
elect the candidate whose worst defeat is smallest.

Juho