[EM] General PR question (from Andy Jennings in 2011)

Kathy Dopp kathy.dopp at gmail.com
Sat Oct 4 09:52:09 PDT 2014

On Sat, Oct 4, 2014 at 12:14 PM, Toby Pereira <tdp201b at yahoo.co.uk> wrote:
> My problem is not that adding the third faction (C) means that the final
> seat might go to C, but that adding C means that the relative merits of
> giving the seat to A or B changes.

I do not understand your concern.  If another faction of voters and
their candidates join the election and obtain enough votes to merit a
seat by changing the proportions of votes all other factions and their
candidates receives, the third set of voters and candidates are
*relevant* and should obtain a seat.  This is not a case of an
"irrelevant" candidate or group of voters since the candidate, in the
case of achieving 1/9th of the votes, this group merits a seat next
after the other two factions' have, together, elected 3 candidates.

> In that respect, C is an irrelevant

Given your prior example:

5: A1, A2, A3, A4
3: B1, B2, B3, B4
1: C1, C2, C3, C4

How are you redefining the word "irrelevant" to label voting group C
as "irrelevant"?

The accepted definition of "irrelevant" among voting methods experts,
is that a *nonwinning* candidate (not a voting group) alters what
other candidates would otherwise win. Group C elects a winning
candidate (given a proportionately fair system) so is clearly it is
*relevant*. Of course it *should* change the results if group C does
not participate because there is, thus, another available seat for the
other two factions to vie over.

You seem to be developing an entirely new condition I have never heard
of that winning candidates are irrelevant if the results change (as
they obviously must) if the winning candidate does not run for office.

I do not agree with your new, unusual definition of "irrelevant", nor,
I believe, would the vast majority of persons who study voting methods
agree with your new condition that a winning candidate, if they do not
participate in the election would alter the results for other
candidates, given the number of seats remains constant.

> alternative so we should be able to ignore that faction. Just to make it
> clear, C would also tie for the final seat with A or B if the other of A and
> B weren't present under your system. So as before, we have:
> 5 voters (A): 2 seats
> 3 voters (B): 1 seat
> and one seat left to assign. According to your system, it should go to C.
> However, let's see what happens if we eliminate the B faction and its one
> seat. We now have:
> 5 voters (A): 2 seats
> and one seat left to assign to either the A or C faction.

You are, then, entirely changing the number of seats to assign from 4
to 3?  That should change something don't you think?

If there were four seats, and factions with, respectively 5 and 1
voter, 3 seats go to the faction with 5 voters, and 1 goes to the

The fact that B
> has gone should not affect which of A or C has the stronger claim to this
> seat. At least, that's what I think. What do you think? But what do you
> think actually happens? The ideal share (of 3 seats) is:
> 5 voters (A): 2.5 seats
> 1 voter (C): 0.5 seats
> With both factions now exactly half a seat away, your method would award a
> tie (every voter will be half a seat away from proportionality under either
> result),

Yes. As does, I would expect, any method trying to achieve
proportionality such as the Sainte-Laguë and D'Hondt methods.

> so removing an irrelevant alternative has changed the result. You
> seem to have a lot of confidence in your method, but I would argue that it's
> minimising the wrong thing. It may be approximately proportional, but it
> seems to break down in certain circumstances.

My method is exactly proportional, not minimizing the "wrong thing",
and behaves exactly as it should if an "irrelevant" candidate, defined
in the normal way as a *nonwinning* candidate, drops out of the

I am flabbergasted to know how you expect a winning candidate to drop
out of a contest, given voters are electing the same number of seats,
without altering the number of seats the other voting groups elect?
You must, as you show above, reduce the number of seats to produce
that nonadjustment.

> Also, it still has the problem I mentioned in another post that it only
> seems to work when there is no overlap between factions, so it appears to be
> just a party list apportionment method and won't work for approval voting
> with free choice.

Yes. Perhaps the algorithm I gave today is too simple and only works
for nonoverlapping groups.  There may be a more complex algorithm that
works, but in the case of overlapping combinations of candidates
chosen by voting groups, I prefer minimizing the formula I gave rather
than trying to develop a more complex algorithm.

Selecting the winning group of candidates that minimizes the formula
I gave will ALWAYS produce the most proportionate representation as is
possible for any set of approval voters, given that sometimes there
will be ties for the most proportionate as possible set of winning

Kathy Dopp
Town of Colonie, NY 12304
 "A little patience, and we shall see ... the people, recovering their
true sight, restore their government to its true principles." Thomas

Fundamentals of Verifiable Elections

View my working papers on my SSRN:

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