[Election-Methods] RE : Re: Re: rcv ala tournament

Dan Bishop danbishop04 at gmail.com
Sun Dec 30 17:42:35 PST 2007

Juho wrote:
> Kevin Venzke replied to Rob Brown:
>> You say you don't see much point in discussing various Condorcet  
>> methods.
>> The ones that I don't like have the quality that sometimes when the
>> quantity of voters who rank candidate A, and don't rank candidate B  
>> at all,
>> is larger than the quantity of voters who rank B at all, B can  
>> still win.
>> Here is a simple example:
>> 7 B>C
>> 5 C
>> 8 A
>> What do you think? Is there good evidence and logic available for a  
>> method
>> to decide that B is the best candidate to win?
> Kevin, you maybe already know/guess my answer. B is only 2 votes  
> short of being a Condorcet winner. C would need 3 and A 5 votes.
Other ways of looking at it are:

* The largest subset of ballots among which B is the Condorcet winner 
has 18 voters, compared to 17 for C, and 15 for A.  (Just like your 
argument, but with subtraction instead of addition.)
* If truncated ballots were disallowed and people flipped coins to 
decide between the bottom-ranked candidates, then B wins with a 
probability of 43.19%, compared to 30.51% for C and a mere 0.45% for A.
* Margins makes more intuitive sense than Winning Votes.  The latter is 
equivalent to assuming that the people who didn't vote a preference 
between two candidates would have unanimously voted for the pairwise 
loser.  The former is equivalent to assuming that they'd split their 
vote equally between the two, which is MUCH more likely.

Of course, electing C would make sense if...
> In your comments I note that you may think that listing a candidate  
> (higher than default bottom) has a special meaning. If there is  
> something like an implicit approval cutoff after the listed  
> candidates (=> 7 B>C>>A, 5 C>>A=B, 8 A>>B=C) then that should be  
> explicitly mentioned. The used method could in this case count both  
> the pairwise preferences and the approvals (A and C would be more  
> approved than B), and the result could be something different than  
> with pure ranking based ballots.
But I see no justification for automatically assuming that "ranked" 
means "approved".

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