# [EM] Instant Approval Runoff or Instant Freedom Voting

Forest Simmons fsimmons at pcc.edu
Wed Mar 14 11:45:36 PST 2001

```I would like to elaborate on (and qualify) two important points before
everybody jumps all over me.

First the following statement needs elaboration and qualification:

> By the way, I believe that WIIA models reality faithfully to the extent
> that the voters are rational, consistent, and careful in their choices.
> Basically it says that we can infer from Dyadic Approval ballots what
> the voters' approval choices would be in an approval runoff.

The "consistent" part would be possible only if the voters had perfect
information ahead of time. In reality, each voting episode also serves as
a poll which informs the voters' strategic probabilities (the Pij's) for
the next round.

Any runoff simulation (including IRV) suffers from this defect.

The next elaboration and qualification concerns this paragraph:

> Dyadic Approval is a matrix method, so the ballots can be scored
> once and for all in matrix form, and the matrices added to get one
> matrix containing all of the needed information.

Well Instant Freedom Voting is a kind of matrix method too, if you allow
matrices with N*2^N entries (where N is the number of candidates). For
each candidate you would have to have an entry recording how many labels
of each type, and there are 2^N different possible labels when there are N
candidates.

On Wed, 14 Mar 2001, Forest Simmons wrote:

> Tom Ruen has recently reminded us of the possibilities of Approval Runoffs
> or "Freedom Voting" in committee meetings and similar situations.
>
> For the record I would like to explain how this type of runoff can be
> simulated instantly from Dyadic Approval ballots as easily (and
> accurately) as IRV simulates simple minded plurality runoff from
> preference ballots.
>
> Recall that Dyadic Approval ballots express an hierarchy of approval in
> one of two equivalent ways.
>
> For example a voted ballot could look like this:
>
> A > B >> C,D > E,F,G >>>  H > I,J >> K > L,M,N
>
> Or the same preferences could be expressed like this:
>
> 111 A
> 110 B
> 101 C,D
> 100 E,F,G
> 011 H
> 010 I,J
> 001 K
> 000 L,M,N
>
> We interpret either ballot as follows: A through G are approved, while the
> rest are not approved. And if all of the approved candidates dropped out,
> H through J would be approved, and the rest not approved. If all of the
> candidates except C through G dropped out or were eliminated, then C and D
> would be approved, but not the others. Etc.
>
> Our instant version of Freedom Voting will be a faithful model of the
> method that it simulates to the extent that the following Weak
> Independence of Irrelevant Alternatives (WIIA) condition holds true.
>
> If a candidate is eliminated from an Approval ballot, that ballot is still
> valid for the remaining candidates UNLESS the eliminated candidate was the
> last one in her category (i.e. last approved or last rejected).
>
> Here's how to do the runoff given the Dyadic Approval Ballots:
>
> 1. Convert all of the ballots to the second form, with all of the approval
> code labels left justified. (Some ballots may use more levels of hierarchy
> than others.)
>
> 2. Simulate an Approval election using only the leading (left most) bit of
> each approval code label.
>
> 3. Eliminate the candidate with the lowest approval score.
>
> 4. Cross out that candidate from each ballot, and her code label if she
> was the last one with that label.
>
> 5. If the change in a ballot results in all of the leading (most
> significant) bits being the same, then delete all of the leading bits.
> Repeat if necessary until at least two labels have different leading
> bits.
>
> 6. Simulate another Approval election using only the leading bits.
>
> 7. Remove the least approved candidate, and adjust the ballots as before.
>
> 8. When a ballot reaches the stage where all of the bits of all of the
> labels are crossed out, that ballot may be archived.
>
> 9. Repeat until one candidate is left.
>
> In Tom Ruen's version of the Approval Runoff half of the candidates are
> eliminated each time, instead of just one.  If the Instant Approval Runoff
> ballots are being hand processed, that option would save some time,
> otherwise there is no need for it.
>
> I believe that this method would pick the same winner as Dyadic Approval
> most of the time.
>
> The main advantages of Dyadic Approval over Instant Freedom Voting are ...
>
> (1) Dyadic Approval is a matrix method, so the ballots can be scored once
> and for all in matrix form, and the matrices added to get one matrix
> containing all of the needed information.
>
> (2) Dyadic Approval results in an ordered list of the candidates like the
> one Hugo Harth was requesting.
>
> (3) Dyadic Approval doesn't require the WIIA (Weak Independence of
> Irrelevant Alternatives) assumption that Instant Freedom Voting
> requires.
>
> On the other hand, Instant Freedom Voting may be easier to understand for
> the average voter.
>
> By the way, I believe that WIIA models reality faithfully to the extent
> that the voters are rational, consistent, and careful in their choices.
> Basically it says that we can infer from Dyadic Approval ballots what the
> voters' approval choices would be in an approval runoff.
>
> Methods that use preference ballots to infer voter choices in other kinds
> of runoffs must either make similar assumptions or admit that their
> simulation is only approximate.
>
> Whether or not an instant simulation faithfully models some repeated
> voting episode method (dare I say runoff?) the resulting instant method
> may have merit in its own right.
>
> I hope you like this one.
>
> Any questions?
>
> Forest
>
>
>

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