[EM] Some myths about voting methods

[Paul Kislanko]

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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