And of course, for range ballots the expression is log(base 2) X (rounded up) times N=number of alternatives, where X is the maximum value in the [0,X] permissible range for voters to specify for each candidate. For range to be different than ranked ballots, at least one more bit per alternative must be available to record the range, so a range ballot for three candidats needs 9 bits, which is three times as much information as a 3-alternative approval ballot.
The statement that "ranked or range ballots provide more information than approval ballots" is not by any means a "myth." It is a consequence of the definition of information. -----Original Message----- From: [email protected] [mailto:[email protected]] On Behalf Of Paul Kislanko Sent: Saturday, June 06, 2009 1:10 PM To: 'Dan Bishop'; [email protected] Subject: Re: [EM] Some myths about voting methods The number of possible votes is not the same as the amount of information in a single ballot. With 3 candidates, there are indeed 8 possible ballots, but any one ballot can be encoded in 3 bits, since any particular choice requires only that many to represent it. Ranked ballots require 2 bits per alternative (01 = 1st, 10 = 2nd, 11 = 3rd) so the minimum ballot representation is six bits, twice as much information as is contained in an approval ballot. -----Original Message----- From: [email protected] [mailto:[email protected]] On Behalf Of Dan Bishop Sent: Saturday, June 06, 2009 11:21 AM To: [email protected] Subject: Re: [EM] Some myths about voting methods Warren Smith wrote: > 6=3! possible rank-order votes. However, there are 8=2^3 possible > approval-style votes. Since 8>6, we see the approval voting ballots > provided more, not less, > info, than the preferential ballot. > > Now you may say "but two of those approval ballot types, namely > all-yes and all-no, were silly." In that case there are only 6 kinds > of non-silly approval ballot (6=8-2). > Then still, approval provided SAME info as preferential ballot. Not > correct to say > "it is clear that a preferential ballot has more information than an > approval ballot." > > --let me refute some errors/myths here. In a 3-candidate election, > there are Only works if there are a small number of candidates. Factorial grows faster than exponential. 2^10 = 1,024 10! = 3,628,800 2^20 = 1,048,576 20! = 2,432,902,008,176,640,000 ---- Election-Methods mailing list - see http://electorama.com/em for list info ---- Election-Methods mailing list - see http://electorama.com/em for list info ---- Election-Methods mailing list - see http://electorama.com/em for list info
