[EM] Approval is not "one person, one vote"

[Adam Tarr]

Stephane Rouillon wrote:

>I  read Olli's mail last time but I am sorry that I have to disagree with 
>Adam.
>
>Olli showed that putting some restrictions (by the mistress)

What restrictions?  Olli's approach uses regular approval ballots.  You 
don't need any input from the voters after you collect the ballots.  The 
talk about lining up and counting heads was just for illustrative purposes.

>  allows to obtain an equivalent to approval that is conducted as several 
> FPTP rounds. However, these restrictions muzzle some voters at some 
> rounds (read well Adam, some of those kids have to gang behind one of the 
> contestant, they cannot chose).

Your choices are uniquely determined by your ballot, just as in IRV.  You 
vote for a candidate (line up behind them) if you approve that candidate 
and not the other.

>Clearly, during these steps, the process gives a choice to some voters, 
>not to others.

The same is true in IRV.  Consider this equivalent definition of IRV:

"In each round, if there is not a majority first place candidate, then 
compare the two candidates with the fewest first place votes.  The one with 
the least first place votes is eliminated."

In IRV, I only vote on which candidate is eliminated if the top remaining 
choice on my ballot is one of the candidates near elimination.  In 
Approval, I only vote between two candidates if I approve one and not the 
other.

Now, let's compare the "sequential" approach to approval with this approach 
to IRV.  Both will always produce exactly the same winner as they would in 
normal approval and IRV.

In both cases, we pick two candidates out using the same approach.  We then 
look at everyone's ballots, divide the voters into A's supporters, B's 
supporters, and abstentions based on the information on the ballots.  The 
method we use to make these distinctions is different, but that is 
irrelevant to the 1P-1V question since both approaches split the electorate 
into these three groups.  We then eliminate the candidate with fewer votes, 
and move on.  Again, it's the same.

I cannot see any reason why one would be considered compliant with 1P-1V 
and the other would not.  There is no reason.

>In my humble opinion, Olli showed with a great thoroughness (spelling?) that
>approval is not "one person one vote" at every round, thus at a whole.

By your definition, IRV would not be 1P-1V either.  After all, just as in 
approval, there are voters who fail to cast a vote in certain rounds.  And 
I haven't even mentioned exhausted ballots yet.

Quite simply, there is no way to define 1P-1V on the overall election 
method (a function from voted ballots to a winning candidate) such that IRV 
passes and Approval fails.  There are many ways one can count ballots and 
get the same results, and I can always choose a pair of approaches for IRV 
and approval where they either both pass or both fail 1P-1V, depending on 
how you define it.

-Adam