[EM] 02/04/02 - Welcome to the Hare camp:

[Donald Davison]

From: "Tom Ruen" <tomruen at itascacg.com>
Date: Fri, 1 Feb 2002 05:49:03 -0600
Subject: [stv-voting] Hare versus Droop - gambled-strategic-betrayal versus
unequally-rewarded-honesty

Dear friends of STV,

I decided to put some bones on my limited theory between Hare and Droop
quotas and see what quotas have to offer from the data on the 2001
Cumulative-Vote Board-of-Directors election at my company.

Note - this analysis has pulled me back on the neglected Hare quota
bandwagon.

QUICK THEORY OF WORST CASES:

Assume fully ranked (nontruncated) ballots, and a 5 seat election.

1. Droop Quota (1/6) - worst case with 6 candidates
A: 16.67%
B: 16.67%
C: 16.67%
D: 16.67%
E: 16.67%
F: 16.65%

5 winners are elected and a 6th loser can stand without elimination just
under the 16.667% quota.

2. Hare Quota (1/5) - worse case with 6 candidates

A: 20%
B: 20%
C: 20%
D: 20%
E: 10.01% (one "weak" winner)
F: 9.99%

4 winners could be elected with the full quota, but the 6th candidate must
be eliminated to free the last-rank of those supporters for E to be elected.
(Other bad cases can exist with more candidates failing the quota, including
the "near equal" 16.67% result in the worse droop quota result at the
opposite extreme.)

One "logic" in support of the Droop quota is to say it is unfair to force
some candidates to make a full quota and others need less (as small as a
half quota) *or* require the dirty use of last-ranks.

We might say the Droop quota is "more fair" for making all winners have the
same support. On the other hand, we might say the Hare quota is "more fair"
for "wasting" less votes on losers. Hare can also be considered more fair
since voters don't gain "surpluses" unless their favorite makes the full
proportion quota.

ACTUAL CV ELECTION DATA: (2001)

There were 5 seats and 6 candidates {A,B,C,D,E,F} so the election was pretty
boring, but the single-loser does make for a harsh line of victory. I
ordered candidates by votes and computed their surplus under both quotas.

Note: Vote counts in CV will be different than STV, but the quotas have
identical meanings for proportionality. CV could, for example, use this
quotas in runoffs of some sort to improve the distribution votes like STV
does more automatically.

1. Using Droop quota: votes/(seats+1)

Total votes=389520
Quota=total/6=64920

Candidate - votes - votes/quota - surplus
E    -    83024    -    1.279    -    +21032
B    -    80787    -    1.244    -    +15867
A    -    72474    -    1.116    -    +7554
F    -    59708    -    0.917    -    -5212
C    -    49584    -    0.764    -    -15336
D    -    43888    -    0.676    -    -21032

3 candidates had the minimum votes needed for election.

Apparently 44453 (11%) unneeded (surplus) votes were wasted on the 3
"winners" in CV.
5696 (1.5%) votes separated the 5th candidate elected in CV and the 6th
candidate not elected.
No excess votes were "wasted" on losers since the droop quota supports one
losing candidate and still elect 5 winners.

Note: The highest two "factions" have a surplus (44k) equal to 7 times as
many votes as separate winners and the final loser (6k)!

2. Using Hare quota: votes/seats
Total votes=389520
Quota=77904
Candidate - votes - votes/quota - surplus
E    -    83024    -    1.066    -    +5120
B    -    80787    -    1.037    -    +2883
A    -    72474    -    0.930    -    -5430
F    -    59708    -    0.766    -    -18196
C    -    49584    -    0.636    -    -28320
D    -    43888    -    0.563    -    -34016

2 candidate had the votes for election.
Surplus votes *might* allow a third winner if nearly all moved to third
highest candidate.
Surplus votes could also theoretically have enough to affect which candidate
is in last place.

Note: The highest two "factions" have a surplus 1.4 times as many votes as
separate the winners and the final loser.

Only by eliminating the 6th candidate can enough votes be freed to elect the
4th and 5th winners, although the actual transfer becomes unnecessary when
we're down to as many candidates as winners.

ANALYSIS

Pro-Droop:

The Droop election at first impression looks nicer to me for not needing to
eliminate any to pick 5 winners among 6. Hare looks unattractive for
requiring some voter's very last rank to get 5 winners at the needed quota.
That is sort of a devious use of ranks it would seem. It's like saying a
candidate in a single seat election got 100% of the vote because no one else
was running! Droop will only use the last rank if all previous ranks have
supported all the winning candidates!

Pro-Hare:

It is clear that the supporters in the highest two winners have *much* more
influence in the Droop Quota - 37,000 surplus votes in Droop versus 8,000
surplus votes in Hare. In both cases they can control which candidate loses,
but they have a lot more power to affect the last winner in Droop as Hare.

Hare is clearly more fair to all voters.

VOTER STRATEGIES?

Droop tends to elect more candidates early so voters are encouraged to
honestly vote their favorite first to get surplus to their second favorites
as soon as possible.

*** Droop offers guaranteed (unfair) rewards (greater influence) for honest
preferences of voters supporting the strongest candidates.

Hare elects fewer candidates immediately and so there is a value for some
voters to consider supporting their weaker favorite(s) first to help them
avoid elimination and hope elimination will transfer enough for all favored
candidates to get elected. (Of course this strategy is *very* dangerous for
individual voters acting alone since their favorite might get eliminated!)

*** Hare offers a gambled chance of rewards (greater influence) using
strategic betrayal of strong favorites.

CONCLUSION:

Hare is fair to all voters since Droop gives more power to voters whom have
already picked winners. (The only way to have more power in Hare is to
gamble on how others will vote.) Do we want to discourage gambling or
encourage honesty?

My response to the itch that makes voters consider ranking weak second
favorite candidate first in Hare-STV is to use tied-ranks and split votes
instead. Tied ranked are not insincere ranking like reverse preference
ranking. Tied rankings is a compromise of split interests, while reverse
rankings is a gambled betrayal.

Arguments I will (cautiously) give to interested coworkers on quotas:
1. Hare quota offers more fair representation, but can encourage some voters
to gamble against a strong "safe" favorite candidate in exchange for power
to protect weaker lower favorites from early elimination.
2. Droop quota gives advantage to sincere ranking due to "extra" surplus
votes awarded on victory.

My recommendation:

We should use the Hare quota and tell voters to "be nice" - don't gamble -
vote honest rank preferences and compromise via tied ranks only if they
*really* want to protect a set of candidates equally.

(My intuition now suggests that the risks will likely *far* outweigh the
uncertain chance for rewards for strategic use of reversed-top-ranks or
tied-ranks/split-votes with STV using the Droop quota.)

I'm sure I've overgeneralized in my quest for deeper understanding, but I
think this analysis is close to the truth.

Any comments or friendly debate?

Sincerely,
Tom Ruen

- - - - - - - - - - - - - - - - - - - - - - - -
Dear Tom,

Welcome to the Hare camp.

Your up coming board election will be more proportional with Hare.

Regards, Donald Davison