# PAD voting

PAD voting is a proportional voting method designed for city council elections; that is, for electing small numbers (5-20) of seats at a time without relying on partisan labels. PAD can stand for either "Prefer, Approve, Disapprove" or "Proportional Approval with Delegation".

Here's how it works:

(Optional:) Before the election, voters and candidates may be **divided into a number of "wards"** that's less than the total number of seats to be elected. For instance, there might be 7 wards and a total of 13 seats. Ballots list same-ward candidates first.

**Candidates pre-rate each other** as "approve" or "disapprove". Candidates may not approve more than half of the incumbents. These pre-ratings are public.

**Voters rate candidates at one of 4 levels: "prefer", "approve", "don't know/delegate", or "disapprove".** (These might also be labeled "good", "OK", "don't know", and "bad".) Default is "don't know". Voters may approve or disapprove of as many candidates as they like, but they are encouraged to prefer only one (though this is not mandatory).

**Any "don't know/delegate" ratings for candidate X are delegated to the preferred candidate.** That is, they are changed to "approve" ratings if over half the candidates Y (, Z, etc.) who were "preferred" on that ballot pre-approved X. Otherwise, "don't know" is changed to "disapprove".

**Define a "quota"** as the number of votes divided by the number of seats, rounded down.

(Optional:) **For each ward, the candidate X with the most same-ward votes gets a seat.** If that candidate has less than 1 quota of "prefer" votes, then remove all ballots that prefer X. If that candidate has more than 1 quota of "prefer", then remove one quota of votes that prefer X. (Which ballots are removed should be based on a single random number, such that each ballot has the same chance of being removed, and approximately the same fraction of ballots from each precinct are removed. In other words, put the ballots in order of precincts, pick a random ballot to start with, and then remove every Nth eligible ballot from there on, with N chosen so as to ensure you go approximately 1 time around the ballots in all.)

If any candidate has over 1 quota of "prefer" votes, they get a seat. Remove 1 quota of their prefer ballots.

**As long as any candidate has over 1 quota of votes combining "prefer" and "approve" tallies, choose the one of those with the most "prefer" votes, and give them a seat.** Remove all their "prefer" ballots, then remove enough of their approval votes to total one quota of ballots removed.

If there is/are still seat(s) left to fill, pick the candidate(s) with the most approvals.

## Summable PAD (alternative version)

The above algorithm requires full data from all ballots. However, it can be approximated using only the following precinct tallies:

- Number of ballots which "prefer" each candidate X, denoted P(X).
- For each pair of candidates X and Y, total of ballot fractions which count as preferring X "first" and which also prefer Y; denoted PP(X,Y). (See below for example).
- Of the ballots counted as first "prefering" each candidate X, number of candidates which "approve" each candidate Y, denoted PA(X,Y). Ballots which prefer no candidate should be included in these tallies as PA(?,Y).

Say that on my ballot I preferred X, Y, and Z; approved of A and B; marked "don't know" for C and D; and disapproved E and F. Say that 2/3 of XYZ pre-approved C, while a different 2/3 of them pre-disapproved D; so that I count as approving C and disapproving D. Thus, my ballot would add to the following tallies:

- P(X), P(Y), P(Z): +1
- PA(X,A), PA(X,B), PA(X,C): +1/3 (since only 1/3 of my ballot is counted for X "first".)
- PP(X,Y), PP(X,Z): +1/3 ("first for X, but also prefers Y and Z")
- PA(Y,A), PA(Y,B), PA(Y,C), PA(Z,A), PA(Z,B), PA(Z,C), PP(Y,X), PP(Y,Z), PP(Z,Y), PP(Z,X): +1/3 (as above, but with Y or Z first)

Note that if a ballot only prefers one candidate, it only adds 1 or 0 to each tally, with no fractions.

Given such tallies, it is easy to approximate the above algorithm. For instance, if P(X) is over one quota Q, and PP(Y,X) is zero for all Y?X, then when electing X you should multiply each of P(X), PP(X,Y) for every Y, and PA(X,Y) for every Y, by the ratio (P(X)-Q)/P(X); this has the effect of reducing P(X) by Q, almost as if you'd eliminated Q physical ballots which prefer X.

## Features

This method obeys "global later no-harm" (a weaker version of later no-harm) in that adding an approval for a candidate with fewer overall "prefer" votes cannot cause the candidate you prefer not to get a seat.

It is good for minority representation:

- If there is a single candidate whom a minority community sees as championing their interests, and the community is large enough to proportionally deserve a seat, then they will be certain to win that seat.
- Even if the minority community isn't big enough to win a seat, their candidate can negotiate with other candidates before publicly declaring pre-approvals. This pre-election negotiation will give the community a fair degree of unified bargaining power; much more so than if each of them had to individually evaluate the other candidates. However, any voter who disagrees with their preferred candidate's pre-approvals is still free to change them.
- If the minority community has several candidates, then as long as those candidates all pre-approve only each other (and the voters don't override that), they will get the total number seats they proportionally deserve.

This method is significantly simpler for the voters than STV. A lazy voter can simply prefer one candidate and leave the rest blank, and that vote will still be an effective vote which is almost certain to help elect some candidate who's closer than average to the voter's preferences. Meanwhile, a highly-engaged voter can give explicit opinions about every candidate in the race, without having to make fine distinctions between candidates of similar quality.

## Related voting methods

Like Single Transferable Vote, PAD is a proportional method based on allocating one quota of votes to each winner using a sequential ("greedy") algorithm. Another feature these two methods share is that they work without explicitly referring to political party, so they can be used for nonpartisan elections.

Like Proportional approval voting, PAD is a proportional method based (mostly) on approval ballots.

Like PLACE voting, PAD is a proportional method which includes delegation and a rated ballot. In the case of PAD, this delegation is merely an optional convenience; in PLACE, it is mandatory. Summable PAD also copies PLACE in that it can be run using precinct tallies; that is, unlike most proportional methods, it is summable.