# [EM] (Fwd) STV and truncation

Steve Eppley seppley at alumni.caltech.edu
Fri Apr 5 19:54:29 PST 1996

```Mike Ossipoff wrote:
>Probably most fractional STV wordings simply leave "exhausted"
>(removed from the election) any vote value of a nontransferable
>ballot.
[snip]
>But there's a better way to do it:
> Where s = the candidate's surplus
> &     t = the combined vote value of his transferable ballots
> &     F = his transfer fraction
>
> F = min (s/t, 1)

I think I can figure out what you mean by 'F' and 't', but it's not
as clear as it could be.

Could it instead be expressed in terms of the number of voters who
didn't truncate?, and the fraction of *their* ballots which transfer?

I'd have to think more about the math than I want to, but I think
there's more involved here in salvaging otherwise wasted votes than
just transfering fractions from winners.  Some ballots won't be
truncated right after a winner with excess, but will go on to rank a
few losers as well.  Some ballots won't rank any winners at
all--salvaging these may be difficult, but the techniques Mike
proposed (distributing the weight of a loser ballot to augment
ballots of similarly minded voters) could be used.

[snip]
>Another possibility, which would require more computation, and
>would be quite out of the question in a hand-count (as fractional
>STV pretty much already is) would be to give voters the option to
>assign the vote value of their exhausted ballots to the other
>ballots in the election which are still transferable and which
>share the same 1st choice.
[snip]

That's one of a family: ... to other ballots which share the same
top N choices.

Example 1: share the same top 2 choices.
Example 2: if a voter truncated after X choices, share the same top X.

--Steve

```