# [EM] Winners or representation?

Richard Lung voting at ukscientists.com
Sun Apr 3 02:54:39 PDT 2022

```It’s putting oneself at an unfair disadvantage to try to prove something
that doesn’t exist. The term “winners” assumes some preordained election
results, that one has to try to discover. The statistical assumption, as
distinct from the determinist assumption, is that there are only best
estimates of representation. Some candidates win beyond reasonable
doubt. Other contests may leave the voters indifferent, with no
candidates a clear winner. This is just a fact of life that defies
mathematical certainty.

Laplacehad a metaphysical belief in determinism. (That is an interesting
hypothesis, as Bonaparte commented.) Yet his adjudication between
Condorcet and Borda appeared in his treatise on probability. Elections
are a statistic. (I follow the account by JFS Ross, in Elections and
Electors.)

Laplacehad the first and perhaps the last word on Condorcet pairing or
Round Robin elections: they don’t take into account the relative
importance of preferences.

Over a century later, in the 1940s, this message was reinforced, by SS
Stevens on scales of measurement. Judging winners solely by binary
elections, staying at the least powerful, nominal scale of measurement,
leaves out a comparison of the whole range of candidates, at once, that
is to say, an ordinal scale of measurement, which preference voting is
the next, more powerful scale. It is the difference between absolute,
all or nothing choice, of a single order of preference, and the relative
choice of a whole range of preferences.

Condorcet pairing may occasionally contradict preference voting. But
this cross-check never departs from minimal choices, which do not
justify a veto over the more general relative choice of preference voting.

Moreover, a case in about 135, like Burlingtonis not statistically
significant enough, to inaugurate Condorcet pairing as an arbiter in
(preferential) elections, considered as statistical estimates.

After the nominal and ordinal scales, Stevens progresses to the
successively more powerful interval scale and ratio scale. These are
both proportional measurements. The only difference is that the interval
scale lacks a real zero. An example is the conventional temperature
scales like Fahrenheit and centigrade. Their different zero points on
the scale are a matter of convention, such as making zero, when water
freezes (either in salt water or fresh-water).

The quota is an example of a ratio scale. Party lists, however are a
particular vote in a general election. Likewise, the local constituency
vote in a national election. The Andrae or Hare system are the more
logical general vote in a general election. The interval scale appears
in voting method, in surplus or deficit of a quota, which sets its
conventional level of zero. A candidate whose votes exactly equal the
quota has a zero surplus and a zero deficit of votes.

The transferable vote possesses all four scales of measurement; a rare
quality in voting methods, which I have long since argued qualifies it
as something like scientific method of elections.

Regards,

Richard Lung.

On 02/04/2022 10:51, Kristofer Munsterhjelm wrote:
> On 25.03.2022 20:50, Richard Lung wrote:
>> I can't help but think that this group is absorbed in determining
>> election winners, rather than representatives of the people, as in a
>> democracy.
> For me at least - I don't know if that's why others are focusing on
> single-winner - it's because multi-winner is so much harder, it's
> difficult to see even where to begin to prove anything.
>
> Take Droop proportionality, for instance. It is known that party list
> methods that are based around fulfilling a quota criterion must fail
> what's called population pair monotonicity (or the Alabama paradox); and
> Droop proportionality implies a sort of one-sided quota criterion, call
> it a lower quota.
>
> But is then Droop proportionality compatible with population pair
> monotonicity? Is it only so for methods that reduce to D'Hondt (which
> passes a lower quota property)? I don't know. Or perhaps population pair
> monotonicity is the analog of the participation criterion, which almost
> all voting methods fail anyway, and thus is not something we need to pay
> attention to.
>
> There are many questions like this. Another one is (strong
> seat-independent) summability: we know of a bunch of methods that are
> summable for single-winner. But is it even possible to pass both Droop
> proportionality and summability for a general ranked voting method?
> Again, very difficult to prove *or* disprove. I have been playing with
> this on and off, and I suspect it is impossible. But I also suspected
> that the combination (for single-winner) of monotonicity and DMTBR was
> impossible, and I was at least partially shown wrong by my optimal
> strategy solver.
>
> The cardinal voting camp has probably been more successful, but they
> have the benefit of being able to treat ballots numerically. Trying to
> do so with ordinal ballots usually leads to clone dependence, Condorcet
> failure or similar problems.
>
> There's also an argument that the best representatives of the people are
> a representative sample of the people, i.e. that one should not elect at
> all, but just populate the representative body with an unbiased
> selection of all kinds of people who make up society. If so, then
> large-scale PR is "solved" by removing the need to solve it by elections
> in the first place. On the other hand, this might also make the question
> of a good single-winner method moot as well, since parliamentary
> procedure is usually very simple.
>
> That's not to say I've been completely uninterested in multi-winner. My
> first post here showed tradeoffs between proportionality (in a simple
> yes-no model) and total satisfaction: to some degree, if you please each
> faction more, you end up pleasing all of society less as the faction
> representatives become more polarized.
> be an obvious result in retrospect, but the gap between social optimum
> and known methods shows that there's potentially a lot more improvement