[EM] STV's rejection: it's "not a defect, it's a feature!"

[Bart Ingles]

Craig Carey wrote:
>
> The Approval Voting method, according to Mr Ossipoff, needs to be
>   considered undefined when this is not true: there are very few
>   candidates and only one winner is to be elected. Is that a viewpoint
>   of others, e.g. Bart?. It is bit like the gaps in the output winner
>   set of Condorcet, except that in the case of the Approval Voting
>   method, everbody knows what the definition is but defers to whatever
>   crumbs of assertions the authorities were able to give.

I have never seen Mr. Ossipoff make the statements claimed here, but
maybe I missed something.  Speaking for myself, I would not agree with
either of the two statements above.

There is no reason to think that approval voting wouldn't work perfectly
well for electing more than one candidate, except that it is not a
proportional system.  For all practical purposes, the 'block voting'
method commonly used in U.S. council-type elections is the same as
approval voting.  

When there are many candidates, STV's performance, both in terms of
selecting Condorcet winners, and in selecting a winners that voters
would express satisfaction with, can decline drastically.  Using
Merrill's spatial models in two dimensions, and *with no polling
information available*, approval voting has a higher likelihood (than
single-winner STV) of selecting a Condorcet winner whenever there are
seven or more candidates.  If the candidates are more tightly clustered
around the center than the voters are, approval voting is better than
STV with any number of candidates.

Of course, if the top two front-runners are identifiable to voters,
approval voting does a better job of electing Condorcet candidates than
STV in any situation.  Looking back at the elections I've observed
recently (including non-partisan and party primary elections, as well as
partisan general elections), I would say that it's fairly rare that the
top one or two candidates would _not_ be identifiable.

> [...]
> Now the Approval Voting method is as far as I can tell, undefined
>   for greater than 0.9999999 [7 nines]
>   of all multi-winner [small-ish] elections that can be analyzed
>   mathematically.

The approval voting method is defined for all elections.  What do you
mean by 'undefined'?


> PS. Maximizing some Utility value is an unclear thing since the
>   maximizing is done under constraints. With suitably selected
>   constraints, the aim can be a test that passes only the Approval
>   Voting method. So the idea of maximal utility values able to be of
>   not importance. E.g. suppose it was subject to a strict constraint
>   that proportionality (provided different), was first maximized.
> [...]

You're probably confusing the idea of an individual voter maximizing his
own utility, as intended here, with the social utility vs. Condorcet
efficiency debate I had with Blake. 

The idea of an individual maximizing his own utility, i.e. voting so as
to make the best use of his own voting power, is constrained by the
available choices and the amount of information available.  The idea is
important, since it helps predict what a voter is likely to do in a
given situation, and also shows what a particular voting system's
strategy weaknesses are.