[EM] National Popular Vote & Condorcet

[Raph Frank]

On Wed, Jul 1, 2009 at 10:34 PM, Dave Ketchum<davek at clarityconnect.com> wrote:
>     Approval data - needs thought but my initial thought is as if each
> approval was a plurality vote - does mean a voter approving 2 gets 2 votes
> counted but relative counts per candidate comes out ok.
>     IRV or Range - examples of methods that should be avoided by states
> willing to have their data included - unless they are willing and able to
> convert to a method that is supported.

I would group them as

Plurality:
A vote for candidate A is considered
A>(others)

Condorcet:
Matrix is provided directly

IRV:
Extract as much info as possible, for example

Round 1:
A: 100
B: 82
C: 41
D: 13

100: A>(others)
82: B>(others)
41: C>(others)
13: D>(others)

D elliminated
4 go to A
3 go to B
5 go to C
1 untransferable

Votes are now
100: A>(others)
82: B>(others)
41: C>(others)
4: D>A>(others)
3: D>B>(others)
5: D>C>(others)
1: D (so effectively D>(others)

C would then be eliminated and we would get info about 2nd choices for
C.  One issue here is that C>D>A would not be distinguished from C>A
(as both would transfer to A).

Approval/Range

This are somewhat different versions of the same method.  There isn't
any way to reverse the process back to votes.

You give each candidate a plurality vote of (votes obtained)*[votes
cast/total approval].  This would at least mean that the state
wouldn't be over represented.

If there were 1000 votes cast and the results were

A: 800
B: 400
C: 300
Total 1500

Then, the results would be:

A: 800/1.5 = 533
B: 400/1.5 = 267
C: 300/1.5 = 200

I you assume that voters will use the strategy of vote for their
favourite of the top-2 and all they prefer to the expected winner, you
could estimate the preference table.

It is possible to find a matrix that matches the approval results, but
there wouldn't be a unique one.

For example:

"Add" A's 800 approvals
800: A
200:

"Add" B's 400 approvals

800 split into:
480: A
320: A+B

200 split into
120:
80: B

Total
480: A
320: A+B
120:
80: B

and so on.

That would result in an assumption that  lots of votes cast blank votes.

Another option would be to find the "top-2".  This could be the 2 most
approved candidates, W (winner) and S (second).

It is assumed that W and S voters would not approve each other to the
greatest extend possible.

So, the above example becomes

>From the results:

A: 800
B: 400
C: 300
Total 1500

A and B are top-2, if 800 approved A and 400 approved B, then at least
200 must have approved both.  This assumes

600: A
200: A+B
200: B

This means that every voter is assumed to approve one of the top-2.

The rest of the candidates could then be assumed to be random.

The full process would be

1) Assume all ballots are blank
2) Process Candidates from most to least approved
3) If any ballots are blank, then designate them as approving the
current candidate
4) Distribute any remaining approval for the candidate randomly
5) Goto 2

This gets you a set of approval ballots which is consistant with the
results.  Also, it is likely to be reasonably accurate, based on the
assumption that each voter only approves one of the top-2.

It can be gamed if a party runs 2 candidates, as then every voter is
considered to vote for one of their candidates.

One option would be to fill blank ballots and then ballots approved by
all the other candidates (bar the most approved).