Distribution of Surplus

[ivnryn]

Apparently, it is the fairest system of them all.

Borda is not the fairest system of all. It is not independent of clones, i.e. a party does better by running multiple candidates. Also, under your proposal, it isn't even a proportional method.

For example, assume there were voters

4: A1>A2>A3>A4>A5>B
4: A5>A4>A3>A2>A1>B
10: B>A1>A2>A3>A4>A5

A1: 4*1 + 4*5 + 10*2 = 44
A2: 4*2 + 4*4 + 10*3 = 54
A3: 64
A4: 74
A5: 84
B: 4*6 + 4*6 + 10*1 = 58

With 2 seats, A1 and A2 win both seats. However the A 'party' is only supported by 8 of 18 voters. In such a case, the fair result would probably be one from each party, if there are 2 seats ... which is what PR-STV would give.

[ivnryn]

Interesting Peter, but dependent on the ballot paper being completed entirely..........otherwise all the independents would be elected...maybe that's your idea...

good luck today..

Unranked candidates are considered equal last, so if there are 13 candidates and you rank one, then all the others get 13 points from you.

In fact, normally Borda gives each candidate a score (number of candidates + 1 - ranking). Un-ranked get 1.

In a 5 candidate race, it would be:

1st: 5
2nd: 4
3rd: 3
4th: 2
5th: 1

[nuj]

Lassies and lads - the system works.

Just vote.

[osuilleabhain]

Apparently, it is the fairest system of them all.

Borda is not the fairest system of all. It is not independent of clones, i.e. a party does better by running multiple candidates. Also, under your proposal, it isn't even a proportional method.

Ivnryn,

interesting. As always, I don't claim infallibility by any means.
However, to poke one hole in the example you give: two seats for
an electorate of 18 is extreme. All systems will work and their true
characteristics emerge only when there are a large number of voters,
compared to number of seats.
Also, the vote-splitting strategy you cite is already practised
(very skilfully by FF) in the PR-STV system, whereby a "sacrificial"
second candidate draws votes away from the rest and transfers
to your party in the hopes of winning 2-3 seats in each constituency.

Speaking of which, is there anyone out there who knows or can
show that it is in fact, FF's skilful 2-3 candidate strategy that has
resulted in their electoral dominance down the decades?

E.g., I don't quite understand why Ruairi Quinn is not paired with
a young Labour candidate in DSE "for the future" and for the sake
of bolstering transfers?

Apologies if long-winded. I already voted. I have time now to
relax and learn more.

Peter
http://www.d246.org

[Electrolite]

I think the most logical way to understand the transferable vote system is to bear in mind that the purpose of your vote is to elect one, and only one, candidate.

If you have given your no. 1 preference to someone who is elected, then your vote has succeeded in its purpose and has, in most cases, reached an effective dead end. The random distribution of a surplus is a valid way for the voters' true wishes to be followed, i.e. that our primary decision is that we wanted this person to be elected and, if there's any "spare change", so to speak, let it go to the next preference we have indicated.

On the other hand, when you vote for a candidate who has been eliminated, your vote still exists in its entirety and will try to comply with your wishes, i.e. to elect your highest preferred remaining candidate who has not already been elected.

All seems fair enough to me!

[ivnryn]

interesting. As always, I don't claim infallibility by any means.

Sorry, didn't mean offense. (I post sometimes to an election methods list and that claim would get a similar response there as Borda isn't seen as that great )

However, to poke one hole in the example you give: two seats for
an electorate of 18 is extreme. All systems will work and their true
characteristics emerge only when there are a large number of voters,
compared to number of seats.

You could add 4 zeros to the vote totals I gave in my example and the problem would still exist. Fundamentally, the problem is that 2 identical candidates will tend to get a boost in their totals. This is called the independence from irrelevant alternative criteria.

Apparently, when Borda heard of this problem, he responded something like "my method is only for honest men".

It may not be an unreasonable method if somehow parties could be prevented from running multiple candidates. However, that is not possible in practice (what is a party and what is a reasonable number of candidates). I think it was used in Ancient Rome or maybe Greece.

The proportionality problem is even more fundamental. It would give nearly all the seats to the majority (or more likely the party which has boosted its votes to a majority by running the most candidates).

Also, the vote-splitting strategy you cite is already practised
(very skilfully by FF) in the PR-STV system, whereby a "sacrificial"
second candidate draws votes away from the rest and transfers
to your party in the hopes of winning 2-3 seats in each constituency.

This is caused by exhausted ballots. It is my opinion that the quota should be re-calculated after each round to take them into account. It is not fair on the voters that one candidate gets elected for a full quota but 2 others get in for only 80% of a quota. In that situation, it would be fairer if they all needed to get 93% of a quota. Vote management is designed to take advantage of this unfairness.

However, this would mean an increase in complexity for the count (but not that much). Surplus would need to be distributed for all elected candidates after each count. (e.g. if the quota drops by 100, then 100 additional votes should be transferred from any already elected candidate).

In fact, it is probable that just doing it once before the last round would fix most of the problem. Before eliminating the last candidate, the quota would be recalculated and surpluses redistributed.

For example, assuming

the quota is 1000
2 seats to be filled

This is the state before the final elimination:

A1: 1000 (elected)
A2: 850
B: 900

Under the current rules, A2 is eliminated and B wins the 2nd seat. However, that isn't fair on the 'A' party. B was elected with only 900 votes while A1 was elected with 1000 votes (in effect the B party's supporters get around 10% more bang for their votes).

Under my suggestion, the quota would be recalculated

(1000+850+900)/(2+1) = 917

A1 drops to 917 (83 surplus)

This is passed to A2 (assuming party loyalty).

The result becomes:

A1: 917 (still elected)
A2: 933 (exceeds quota, so elected)
B: 900 (eliminated)

A1 and A2 are elected. This is fairer as both A1 and A2 were elected with the same quota of 917. B didn't get enough votes to achieve the quota.