[EM] Re: Range Voting

[Forest Simmons]

>Date: Fri, 07 Jan 2005 08:31:30 -0800
>From: Mike <mrouse1 at mrouse.com>
>Subject: [EM] Thanks to a couple of list members (Condorcet/Range
>	completion	method)
>I'd like to thank Chris Benham for providing me the links to James 
>Green-Armytage's site, which answered a lot of my questions.
>
>I might as well ask another question, since this one went so well: Has 
>anyone tried replacing Borda with Range voting in methods like Borda 
>elimination or Nanson to see what the properties and paradoxes were?
>

Mike, sequential elimination always introduces the same basic strategy 
problem that IRV has: you attempt to help a compromise candidate 
survive to the last round at the expense of candidates that you prefer, 
because you have reason to fear that your favorite(s) would not fare as 
well in the last round as your compromise.

To counter this problem the idea of "Runoff Without Elimination" has 
been proposed independently by various people (even Donald, of all 
people).

RWE requires that in the final stage, all of the candidates who have 
been eliminated are put back into the pool.  The runoff stages are just 
for gathering information about relative probable success of the 
candidates.

For example, you could do the runoff that you suggest, and then (after 
your final stage) put all of the candidates back in the pool, and 
calculate an approval cutoff on each ballot based on a weighted average 
of the candidate ratings on that ballot.  The weights (for example) 
could be proportional to the square (for example) of the number of 
stages survived by the respective candidates.

There is no particular incentive to have your favorite survive too many 
rounds, since the one who survives the most rounds is squarely in the 
cross hairs of the other candidates.

Another RWE method would be to use Random Ballot Dutta to get the 
weights:
Temporarily cross off all candidates except the members of the Banks 
set or Dutta set.  Do a symmetric completion of these ballots so that 
each revised ballot has exactly one Dutta candidate in first place. Use 
the first place counts on these revised ballots as weights (for 
approval cutoff calculation) on the original ballots.

What if there is only one member of the Dutta set?  That's a nice 
problem.

I think it would be hard to improve on the performance of this method, 
but it would probably be a harder sell than a simpler version of RWE.

Check out Kevin's "Gradual Information Approval" for a simple, 
appealing method.  In the k_th stage the top n-k approval getters from 
the previous stage are given equal positive weight for an approval 
vote.  In the last (n-2) stage, only two candidates have positive 
weight for the cutoff calculation (so on each ballot the cutoff is 
halfway between them) but the other candidates are still in the action. 
"Where there's life, there is hope."


Forest