Splitting votes, Instant-Runoff-1, a

[Tom Round]

Tom Round wrote:
>>(1)  "INSTANT-RUNOFF-1"
 -snip-
>It seems analogous to the use, in PR-STV, of voters giving
>equal preferences to be split equally
 -snip-

Steve Eppley replied:

> I don't see that analogy.  In IR-1, equal preferences are NOT split.
Each of the equal candidates receives a whole vote.

> PR-STV could also be modified so it doesn't split votes among equally
ranked candidates.  I don't see the democratic value of splitting the
ballots' weights.

               * * * * *

Point taken. What I meant is this ...

I accept that there is a distinction between "N equal
preferences = 1/N of value to each" and "N equal preferences =
full value to each", so far as counting is concerned. I meant
only that they are similar so far as the voter is concerned.

That is, the voter may marginally prefer X over Y, yet still
decide to give an equal preference to both for the sake of
defeating the most-disliked candidate (for a single-seat) or
for maximising the number of seats won by the party team as a
whole (for multi-seat PR).

To the extent that Bentham-style "utiles" or measures of
preference intensity can be reliably determined (even to the
voter herself, let alone to an external observer), it might be
that an "approval rating" of 99% for X, 95% for Y and 2% for Z
leads the voter to mark her ballot, not 1, 2, 3 for X, Y and
Z, but 1, 1 and 2. If she had her druthers in an ideal world,
she'd marginally prefer to elect X over Y, but either is
better than a victory for the evil Z.

                           * * * * *

I assume Steve knows what the analogous strategy is in a
multi-seat election, but just in case other cc'ed readers
don't, here's an illustration:

Assume Big Party has 470 votes, Medium Party has 450 votes and
Small Party has 80 votes, in a race for 9 seats (ie, quota is
just over 100 votes out of 1,000). Assume for simplicity too
that the supporters of each party have a definite order of
preference among the candidates of their respective party
teams, and vote for them in that order, so that the first-
preference votes cumulate on the highest-ranked candidates on
each party's ticket and then flow smoothly down the ticket.

In this case, an ordinary STV count will go something like
this, with the seats won in the order indicated in brackets.
Effectively, one quota is deducted from each party's total
every time it wins a seat:

Big       470 (1st) 370 (3rd) 270 (5th) 170 (7th)  70
Medium    450 (2nd) 350 (4th) 250 (6th) 150 (8th)  50
Small      80        80        80        80        80 (9th)

Big 4 seats, Medium 4 seats, Small 1 seat.

(Of course, there may have been a tight exchange of
preferences between Big and Medium to keep out Small, but if
enough preferences "leak" to Small or go exhausted, then Small
has the best chance of taking the 9th seat.

However, if the Big and Medium party voters had split their
votes evenly among all their candidates at each stage (whether
by the device of equal preferences, or by a Tasmanian-style
rotated ballot-paper, or by distributing rotated how-to-vote
cards), then the result could be quite different.

After an early round of eliminations, each party is reduced to
its "final-contender" candidates, equalling one more than the
number of full quotas in that party's total - and, remember,
with the votes divided equally. (No one has yet reached quota
and been elected):

Big       470  =    5 candidates with 94 votes each
Medium    450  =    5 candidates with 90 votes each
Small      80  =    1 candidate with 80 votes

This way, the Small candidate will be the first one eliminated
of those still remaining, and she cannot win the final seat.
The result will be 5-4 for Big and Medium, or vice versa
according to how Small's preferences flow.

tOM

-------------------
Overflow-Cc: 100245.2440 at compuserve.com ('Geoff Powell'),
   afreeman at acslink.net.au ('Andrew Freeman'),
   bmusidla at email.dot.gov.au ('Bogey M'),
   c-p-r at netcom.com ('Citizens for Proportional Representation'),
   crabb.deane at pi.sa.gov.au ('Deane Crabb'),
   dunnmj at ozemail.com.au ('Martin Dunn'),
   election-methods-list at eskimo.com ('Election methods'),
   GGoode at VTRLMEL1.TRL.OZ.AU (Goode, Geoff),
   j.pyke at qut.edu.au (John Pyke, QUT Law School),
   jhtaplin at cygnus.uwa.edu.au ('John Taplin'),
   lee at cs.mu.OZ.AU ('Lee Naish'),
   martinw at cse.unsw.edu.au ('Martin Willis'),
   mdt at ozemail.com.au ('Matthew Townsend'),
   voting-systems at netcom.com ('Voting-systems')