[EM] STV and having quotas to eliminate losers

[Craig Carey]

Modifying or repairing STV.


STV as a method has regions in it where it is very unsatisfactory, i.e.
 it now and then can do things like reward politicians who campaigned
 hard, with a loss at the election. ("Voting for candidate A vote
 causes candidate A to lose"). Similarly, speaking ill of a competing
 candidate could harm his public reputation by an amount sufficient to
 cause that opponent to win.

The problem being noted here is due to the eliminating of losers one by
 one at each stage. It would be better [unproven] if the eliminating of
 the remaining candidates (on the basis of their 1st preferences)
 was done on the basis of whether they meet the quota or not.

The quota in IFPP suggests that in one winner STV (i.e. the
 Alternative Vote method, AV), the quota ought be 1/N times the total
 number of votes, where N is number of candidates remaining.

Probably a mayor's office (or a single electorate with a PC) could
 have the optimal divisor for the quota determined within a week or
 two. It might be asked: why not use algebra?. A response could be that
 STV is so arbitrary, so distant from what is optimal, and also
 seemingly very complex to mathematicians, that using algebra rather
 than numbers could lead to no results or results that are not much
 better than simulations could find.

A possibility is to have a 8 winner 30 candidate problem, and have a
 partially random tour through the simplex and find out what fraction
 of the line segments exhibited a (P1) failure, e.g. where a candidate
 lost when holding the first preference but won when it wasn't given
 a preference or the preference was shifted away from being the first.

It could be imagined that being actually elected under STV or AV, is
 rather disagreeable event. FPTP's has its vote splitting problem.

Here's the simplest example showing that STV can make a vote for a
 candidate cause the candidate to lose.

Note that Candidate C loses when it has the first preference in
 2 papers, but it wins when it does not.

: ------------------------------------------------
: 
:   5 AB
:   6 B.
:   8 C.
:   2 C.        <--- B wins, in the STV method
: 
: STV: B
: IFPP: C, FPTP: C
: 
:   5 AB
:   6 B.
:   8 C.
:   2 AB       <--- C wins, in the STV method
: 
: STV: C
: IFPP: C, FPTP: C
: 
: ------------------------------------------------

I note that applying quotas to losers (with a different quota at each
 eleimination stage), wouldn't fix the problem where votes are wasted
 because of transfer values. Under that consideration, STV is more
 like FPTP than it need be.





--------------
ADDITIONAL:

At 15:07 11.10.99 , David Catchpole wrote:
>I expressed a "criterion" or "modification" in the message which applies
>generally. The use of W' is this- consider system W and schema V. Take all
>proper subsets of candidate lists for V. Is there an electoral system W'
>such that W' of V is independent of the removal of irrelevant alternatives
>to W of any proper subset? If so, then W must be such an electoral system.

A note to Mr Catchpole: The reformulation of IIA now has these
 words: "removal of irrelevant alternatives". What is wrong with
 the word "loser", and the word "preference", and "candidate"?.

 The IIA theory collapsed over a tiny 5 voter example, and while
 there may be a few more IIA versions not yet released, surely
 the idea doesn't need the garb of incomprehensible English that
 is so vague that none can be sure whether they could translate
 it into a logic expression in a fully correct way?, something
 that is accessible to the intellience of all?.



Craig Carey, 1 October 1999