[EM] Re: Rewording Strategy A (BF(1st))

[Rob LeGrand]

Forest wrote:
> This wording is the best I've seen for introducing the concept,
> but it doesn't tell what to do when (1) neither of the two
> frontrunners is preferred over the other by the voter, or what to
> do in the case (2) when the two frontrunners are considered
> equally likely to win.

I define my strategy A in the following way, which covers those two
cases.  It assumes input of an array Poll, where Poll[i] is the
number of approval votes for candidate i in the latest poll, and an
array Util, where Util[i] is the focal voter's cardinal utility for
candidate i's winning the election.  There are k candidates.

let TopPoll[i] be the sorted elements of Poll[i] so that TopPoll[1]
   is the largest number in Poll and TopPoll[k] is the smallest
set TopNum[i] and TopUtil[i] to 0 for all i between 1 and k
for i between 1 and k do
   for j between 1 and k do
      if Poll[i] >= TopPoll[j] then
         add 1 to TopNum[j]
         add Util[i] to TopUtil[j]
for i between 1 and k do
   set j to the smallest number between 1 and k such that
      Util[i] * TopNum[j] is not equal to TopUtil[j]
   if Util[i] * TopNum[j] > TopUtil[j] then
      approve candidate i

This algorithm effectively handles your cases (1) and (2) the same
way you did.

I regret not having time to be more active on the list.  So often I
have saved a post that I plan to respond to and never get back to
it.  This semester I'll have even less time, as I'm teaching a
software engineering class in my computer science department.  One
team's project is an online voting laboratory that will allow an
election administrator to run several different kinds of online
elections, including many variants of DSV.  If anyone on the list
has suggestions for possible features of such a software product,
let me know privately.  Thanks!

=====
Rob LeGrand, psephologist
rob at approvalvoting.org
Citizens for Approval Voting
http://www.approvalvoting.org/


		
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