[EM] Some myths about voting methods

[Paul Kislanko]

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: election-methods-bounces at lists.electorama.com
[mailto:election-methods-bounces at lists.electorama.com] On Behalf Of Paul
Kislanko
Sent: Saturday, June 06, 2009 1:10 PM
To: 'Dan Bishop'; election-methods at electorama.com
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: election-methods-bounces at lists.electorama.com
[mailto:election-methods-bounces at lists.electorama.com] On Behalf Of Dan
Bishop
Sent: Saturday, June 06, 2009 11:21 AM
To: election-methods at electorama.com
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

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