# Two fairer(?) variations of STV

Steve Eppley seppley at alumni.caltech.edu
Sun Feb 16 11:55:15 PST 1997

```[This message is mainly intended for Tom Round and the folks he
often cc:'s.  I'm not an expert on STV, so perhaps the variations
below aren't new--I hope I'm not wasting anyone's time with this.
If there's something new and useful here, Ed Still can forward it
to CV&D.]

Two common variations of STV, as I understand it, are "random
deletion" and "equal fraction deletion" when a seat-winner exceeds
the needed quota.  (I'm probably not using the right terminology.
Maybe it's more common to think in terms of transfer instead of
deletion.)

To me, it seems intuitively unfair that the ballot of a voter who
ranked many other candidates ahead of the seat-winner should have
as much transfer weight deleted as the ballot of a voter who ranked
the seat-winner in first place.  I think that an important axiom
of representation is:

A voter is likely to be represented better by his/her
mth choice than by his/her nth choice, if m<n.

(Note: this axiom isn't relevant to single-winner elections.)

The voter who ranked the seat-winner high (higher=better) is more
likely to be represented better by the seat-winner than is the voter
who ranked him low, suggesting that the latter voter needs more
representation from other seat-winners than the former.

Here are two variations which pay attention to this principle,
but they may be unsuitable if the voters are devious enough to
order-reverse (e.g., some voters may misrank their favorite low
if they can reliably predict it's a sure winner):

1. Iterative deletion in preference order

Delete the ballots in order of how high they originally ranked the
seat-winner.  This is an iterative deletion process, beginning with
the ballots which ranked the seat-winner in first place.

At some point in the deletion iterations, the number of ballots
still needing to be deleted (nD) may be less than the number of
ballots which ranked the seat-winner in Nth place (nN, where
N is the iteration level).  At this point, either "random" or
"fraction = nD/nN" could be used to delete some of those ballots
which ranked the seat-winner Nth.

If the STV count is being performed using low-tech, such as by
piling up ballot cards according to which of the non-eliminated
choices they rank best, this variation would be of comparable
quickness as "random" and of course much easier than "fractional".
Whenever a candidate is eliminated, each ballot in its pile would
be transferred to the *bottom* of the pile of the non-eliminated
candidate it ranks next.  (For randomness, ballots being transferred
to the same pile should be shuffled before being put under the pile.)
The quota of a winner would be deleted from the *top* of its pile.
(For randomness, the initial piles could each be shuffled before
the tally begins.)

2. Non-iterative "non-equal fraction" transfer

The fraction of weight transferred depends on how high the ballot
ranked the seat-winner.  (Reasonable formulae for the appropriate
fraction are yet to be determined.  I won't have time to pursue this.)

* * *

One final thought-- if preferential deletion is used, then the
"Condorcetish" multiwinner prop rep method we discussed some months
ago may perform better than if it uses "random" or "equal fraction"
deletion, on the representativeness principle cited above.  Using
"multiwinner Condorcet With preferential deletion", the ballots which
ranked the Condorcet centrist compromise high (best) will be deleted
before ballots which ranked it low (worse), so the undeleted "wing"
voters will have more chance of electing their favorites.

I say "may perform better" instead of "will perform better" because
a devious electorate's order reversal could play havoc with fair
deletion.  Voters who like the Condorcet winner best might rank
him/her low.

```