Re: [EM] [CES #9066] My Quora answer on egypt and voting systems

[Abd ul-Rahman Lomax]

At 08:37 PM 7/5/2013, Jameson Quinn wrote:
http://www.quora.com/Egyptian-Military-Ousts-Mohamed-Morsi-July-3-2013/What-were-the-primary-reasons-that-the-Egyptian-military-removed-Morsi-from-the-Presidency/answer/Jameson-Quinn 



Nice answer, Jameson. 



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Re: [EM] A more Condorcet-like party list PR method

[Kristofer Munsterhjelm]

On 07/06/2013 02:26 PM, Kristofer Munsterhjelm wrote:


The method should be weakly summable (i.e. when the number of parties
are kept constant). For each cell in the matrix, do the elimination
first, then store the counts for each party. These counts can be summed
up between districts, so if n is the number of parties, you have (2^n)^2
cells, each of which stores n numbers in the worst case. And since n is
a constant, so is 2^n.


Replying to myself with an oops, here. By "weakly summable", I usually 
mean "summable with the number of seats held constant, number of 
candidates permitted to vary". If by "candidates" we mean parties, the 
Condorcet-like party list method fails this. Instead, it has a peculiar 
form of kinda-summability: with the number of candidates (parties) held 
constant but seats left to vary, it is summable.



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Re: [EM] Burlington dumps IRV; Immunity from Majority Complaints (IMC) criterion

[Abd ul-Rahman Lomax]

At 08:13 AM 7/5/2013, Jameson Quinn wrote:
IMC seems to me to be too narrow to be a general criterion, if only 
one custom-built voting system passes it. WIMC is an interesting 
refinement of Condorcet and Smith. But neither belongs on Wikipedia 
without a "reliable" citation.


2013/7/5 <sepp...@alumni.caltech.edu>
Should IMC and WIMC be added to Wikipedia?


The obvious first: Many Wikipedia articles violate Wikipedia policy, 
it's an issue of what one can get away with. If anyone objects, and 
knows how to pursue the process, such articles would quickly be 
deleted. No wiki is considered a reliable source, for starters, nor 
are mailing lists. Neologisms will generally be rejected even if 
there is a single "Reliable Source." But a redirect might be allowed 
for a neologism, if it has widespread usage.


Many *existing* articles are vulnerable to deletion.

As to IMC and WIMC, I'm not going to go into detail, but I have many 
times indicated that there is a problem with resolving an election 
contrary to the wish of a majority. In classical deliberative 
process, *no decision is made -- ever! -- without the express consent 
of a majority of those voting.* That includes, in the basis for 
majority, spoiled ballots, it only excluses *completely blank ballots 
with no mark.* "Scrap paper," Robert's Rules calls them. No majority, 
election *fails.*


Yet we know that it is possible, with a practically-ideal voting 
system (Range), that the optimal choice is not the first preference 
of a majority. So ... we can't just assert as some sort of absolute, 
the Majority Criterion. Rather, a full resolution of this would 
involve another poll. It is possible that if the voting system 
indicates a very weak preference on the part of the majority, under 
some conditions, it might be possible to complete the election. 
Defining those conditions would, however, be relatively complex. It's 
more common that there is no majority preference, only a plurality, 
and, under those conditions, it is well understood that a normal 
solution is a runoff election. So the problem reduces, then, to 
making sure that the nominations for that runoff are likely to truly 
represent the will of the majority, as might be inferred, i.e., that 
they will include a majority preference.


It is commonly assumed that runoffs will have two candidates only. 
That's artificial, for sure, and it sets up finding a majority as if 
it were, itself, an absolute. A good voting system in the runoff can 
handle three candidates, and, remember, a runoff election is a very 
different animal than a primary. The voters will be much more informed.


The point about violating the wishes of a majority is clear: it can 
easily lead to dumping the voting system and other responses, and the 
only way around that would be to *disempower* the majority. Kind of a 
Bad Idea in a democracy, eh? Exactly who does this job, who holds the gun?





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[EM] A more Condorcet-like party list PR method

[Kristofer Munsterhjelm]

Among other things, in Wahlberg's thread, there was a discussion about 
ways of making Sainte-Laguë party list PR accommodate ranked ballots.


The simplest method found was:

1. Allocate seats according to Sainte-Laguë or Webster with respect to 
first preference votes.

2. If any party got zero seats:
2.1. Remove the party with the least votes from all ballots.
2.2. Go to 1.

This will work most of the time, but it has two potential problems.

The first is that when there are only a few seats, it will reduce to 
Plurality (i.e. it doesn't take compromise parties into account).


The second is that the order of elimination may matter. If you have an 
L-C-R situation among parties, and none of them can get a seat by first 
preferences alone, then the compromise C (which may get a seat were L 
and R eliminated) may be eliminated early and so make the outcome worse 
for the L-C-R voters.



After some thinking, I think I've found a hack that should fix the 
second problem. I'm unsure how much it fixes the first, but it reduces 
to Condorcet in the single-seat case.


It's also probably too complex to be used, but that's another matter :-)


So, the method. It works like CPO-STV or Schulze STV: you define a 
function f({x}, {y}) for subsets {x} and {y}. This function produces a 
score of a virtual contest between the two subsets, and then these 
contests become the entries in a pairwise matrix that is run through a 
Condorcet method.


For this method, the subsets are sets of parties. To determine the score 
for f({x}, {y}), do this:


1. Eliminate all parties not in either {x} or {y}.
2. Do a restricted Sainte-Laguë allocation for {x}. A restricted 
allocation goes like Sainte-Laguë, but no party not in {x} can get any 
seats, and every party in {x} must get at least one seat. Implement 
thresholds as needed here.
2.1. If the allocation is contradictory (e.g. more parties than seats, 
or there is a threshold and a party below it has been given seats), then 
treat the allocation as one where no seats were given to any party.
3. Once done, for each party, add the number of voters that voted for 
that party, minus that party's quotient, to a common sum. Call this sum 
{x}'s proportionality score.
4. Do a restricted Sainte-Laguë allocation for {y} and similarly 
calculate {y}'s proportionality score.
5. f({x}, {y}) is equal to {x}'s proportionality score in this contest. 
f({y}, {x}) is equal to {y}'s proportionality score in this contest.


And here's a last-seat compromise example, adapted from the LCR example 
I gave earlier:

100: X
100: Y
 46: L > C > R
 44: R > C > L
 10: C > R > L

3 seats.
Let's determine f({XYR}, {XYC}):
The union of these subsets is {XYRC}, so L is eliminated. We now have:
100: X
100: Y
44: R
56: C

Restricted Sainte-Laguë allocation for {XYR}:
By the one-seat rule, we give one seat to each.
This gives a quotient of 100/3 for X and Y, and
44/3 for R.

The proportionality score is thus:
  100 - 100/3   (X-voters)
+ 100 - 100/3   (Y-voters)
+ 44 - 44/3 (R-voters)
+ 0 (C-voters)
= 488/3

Now, do {XYC}.
Restricted Sainte-Laguë allocation for {XYC}:
By the one-seat rule, we give one seat to each.
This gives a quotient of 100/3 for X and Y, and
56/3 for C.

The proportionality score is thus:
  100 - 100/3   (X-voters)
+ 100 - 100/3   (Y-voters)
+ 0 (R-voters)
+ 56 - 56/3 (C-voters)
= 512/3

So {XYC} wins, as it should.

And an example where the seats aren't all forced by the one-seat rule,
f({XL}, {XC}), again 3 seats:
The union of these subsets is {XLC}, so we have
100: X
 46: L
 54: C

Restricted Sainte-Laguë allocation for {XL}:
By the one-seat rule, one seat has to go to X and one
has to go to L. Now the quotients are 100/3 for X,
46/3 for L, and 54 for C. Since the allocation is
restricted to {XL}, C can't get any seats. Of the
remaining parties, X has the greatest quotient
and gets the second seat.

The final quotients are 100/5 for X, 46/3 for L, and
54 for C.

The proportionality score is thus:
  100 - 100/5   (X-voters)
+  46 - 46/3(L-voters)
+   0   (C-voters)
= 332/3

By the same reasoning, for {XC}, X gets two seats and C gets
one. This gives a proportionality score of 116, which is
348/3 and thus {XC} wins this co

Re: [EM] Burlington dumps IRV; Immunity from Majority Complaints (IMC) criterion

[Markus Schulze]

Dear Steve Eppley,

the following criterion has been discussed several
times in the Election Methods mailing list:

   Suppose a majority of the voters prefers candidate A
   to candidate B. Then candidate B must not be elected,
   unless there is a sequence of candidates from
   candidate B to candidate A where each candidate beats
   the next candidate with a majority that is at least
   as strong as the majority of candidate A against
   candidate B.

The above criterion was called e.g. "beatpath criterion"
or "immunity from binary arguments". The above criterion
is satisfied e.g. by the Schulze method.

Your "immunity from majority complaints" criterion has
the following problems:

(1) To guarantee that only the ranked pairs method
satisfies this criterion, you added the requirement
that each candidate of this sequence must be ranked
ahead the next candidate of this sequence according
to the social ordering.

(2) To guarantee that only the ranked pairs method
with "winning votes" satisfies this criterion, you
added the requirement that the strength of a pairwise
comparison must be measured by the number of voters
who prefer the winning candidate to the losing
candidate of this pairwise comparison.

These additional requirements are not justified
by the original motivation for this criterion:

> Suppose a majority rank x over y but x does not
> finish ahead of y (in the election's order of finish).
> They may complain that x should have finished ahead
> of y, using "majority rule" as their argument. (...)
> So it is desirable to be able to turn their own
> "majority rule" argument against them.

(3) Your criterion presumes that the purpose of an
election method is to create a social ordering.
However, most readers will argue that the purpose
of an election method is to find a winner and not
to create a social ordering.

Markus Schulze


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