Thanks for the thoughtful replies on percentage support.
I think Stephane and Forest's ideas are especially intriguing. At first glance, if applied to Condorcet ballots, it seems they would require Approval cutoffs.
I've thought of continuing to merely total up the first place votes, but the obvious flaw there is that the ordering of first-place totals would not be in Condorcet order. If the selection of the winner would not be accomplished by counting the first place votes, then using the first place votes to communicate how close each candidate is to "winning" is not so meaningful.
(You can get Condorcet order by finding the Condorcet Winner, then eliminating the winner from all ballots and compressing the rankings, and then finding the next Condorcet Winner, etc. Ideally, the percentages should be in the same order.)
As for James' questions, it's obvious that in an election that measures support for all candidates, the voting population is expressing 100% of available "support". The question is how to use that voting method to quantify that support in percentage terms, split for each available candidate. The concept is supposed to be fuzzy, because the question is how to unfuzzify it. As for how to define polling, I mean surveys - either one-time, or "tracking" surveys, that attempt to communicate proportional support in a voting population among several choices. The general intent is to communicate how "close" a variety of choices are to "winning".
We'll never escape the desire to use polling, public support, approval/disapproval tracking, support levels of prospective legislation (etc). We will continue to have the need to express preferences in proportional percentages.
My best attempt at trying to figure this out for Condorcet was the following, similar to Daniel's thoughts:
-Find the Condorcet Order.
-Starting with the first place finisher, find how many preference shifts on all ballots would need to change to replace second place with first place. (If one ballot would require a 4th place choice to be 1st place, that would be three shifts.) Add this number to global variable "x". Register this number as the difference between the two candidates.
-Eliminate the Condorcet Winner, compress and retabulate the ballots, and repeat.
When done you will have a total number of shifts, and a number for each candidate. For example:
A B requires 6 shifts to beat A. C requires 9 shifts to beat B. D requires 5 shifts to beat C.
20 shifts overall. 20 "ticks" between last place and first.
Those numbers would help to determine the distance between the competitors. What is left is to determine the bounds - the floor of support the last-place finisher received, and the ceiling of support the first-place finisher received. That's where I stopped. I also stopped because I couldn't decide whether it was better to determine how many shifts it would take D to beat C, or to instead NOT eliminate the winner each time, and instead calculate how many shifts it would take D to beat A.
I'll review the other ideas and write back with my thoughts.
Thanks, Curt
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