Different reweighting for RRV and the concept of Vote Unitarity

That is a hard question to answer, since free riding cannot be prevented in a PR method, only mitigated. Whether reducing free riding is worth violating a given criterion depends on how much you are mitigating it. @AssetVotingAdvocacy 's proposal

would have created a very large vulnerability for free riding by allowing voters to completely protect their ballot from losing weight while only slightly reducing the amount of support they give to their chosen candidate (e.g. reducing their score of a candidate from 9 to 8 could prevent them from losing any weight whatsoever, but would still contribute 8 points to that candidate).
Unfortunately, I linked to the wrong paper in the quoted post. The correct link was http://9mail-de.spdns.de/m-schulze/schulze2.pdf
The relevant bit is section 4, which describes how parties can exploit free riding vulnerabilities through “vote management” strategies, in which they tell their party members to vote in a way that allows them to use as little weight on their seats as possible. This can harm the independence of candidates from their parties, since for a voter’s vote to count as strongly, they must follow the tactical voting instructions of the party they wish to support, rather than support their favorite members of the party. Parties can adjust their instructions to favor or disfavor their members based on how loyal they have been, resulting in a party list-like hierarchy. Independent candidates won’t have this sort of strategic campaign backing them, causing independent seats to become more expensive, which both makes it harder for independents to be elected and potentially discourages voters from supporting them.

The US equivalent of this is known as the Hastert Rule.

This seems somewhat exaggerated to me. I’d imagine most voters would be okay losing weight off their vote if it allowed them to worry less about this kind of strategy game. And the more tactical voters only have a chance of retaining their voting power, not a guarantee. Still, if we go with Parker’s enhancement (find the Hare Quota of points with fewest voters) this all disappears mostly.

I think the importance of vote management depends on how many winners you have. Note that in the vote unitarity methods, electing a candidate costs 1 Hare Quota. However, you can force your election with just a Droop Quota of bullet voters. The benefit to purchasing seats for a Droop Quota rather than a Hare Quota is no more than 1 seat. If you are electing a national legislature with 105 seats all in a single national district, then the vote management campaign is probably more trouble than it’s worth. The difference between a Hare and Droop Quota is so small that you won’t be able to assign voters to candidates with enough precision to succeed. If you are electing this legislature in several 5-member districts, then there are 21 “last seats” that could be influenced by a vote management strategy, and the difference between a Hare and Droop Quota is large enough to be exploited.

Do you mind making an example for this?

In general, I’d guess that if it’s the last seat, the difference between the “legitimate” winner and the strategy-elected winner would be smaller, and even then the voters may or may not engage strongly in such strategy, since individual pivot probability is so low, and the expressive benefit of honesty is higher. Am I being naive here, or is there a big advantage with strategy?

Here is an example:
49: Party A
51: Party B
5 seats; Hare Quota: 20; Max Score: 5
17 votes: A1 5; 16 votes: A2 5; 16 votes: A3 5
51 votes: B1 5; B2 5; B3 5
The winner is B1. This costs the party B voters 20 votes worth of weight.
17 votes: A1 5; 16 votes: A2 5; 16 votes: A3 5
31 votes: B2 5; B3 5
The winner is B2. This costs the party B voters 20 votes worth of weight.
17 votes: A1 5; 16 votes: A2 5; 16 votes: A3 5
11 votes: B3 5
The winner is A1. This costs the 17 voters for A1 their vote. No one else gave A1 any votes, so no one else loses any weight.
16 votes: A2 5; 16 votes: A3 5
11 votes: B3 5
The winner is A2. This costs the 16 voters for A2 their vote. No one else gave A2 any votes, so no one else loses any weight.
16 votes: A3 5
11 votes: B3 5
The winner is A3. Party A wins 3 seats, Party B wins 2 seats.
Note that this is a problem for any method that has a party list case of largest remainder (Hare quota).

If some ballots vote only for noncompetitive candidates, this increases the Hare quota size without changing the number of votes required to force a candidate’s election. For example, adding 10 ballots marked {Vermin Supreme: 5} increases the costs of the B seats to 22 votes, leaving them with 7 votes after electing 2 candidates. This means that the number of votes needed to force a candidate’s election can fall even below the Droop Quota in practice. If we redid the example election using Droop Quotas rather than Hare Quotas and included the Vermin Supreme votes, then party B would be left with 14.333 votes after winning 2 seats, allowing A’s vote management strategy to take 3 seats.

This is good work Dave. I’ll have to dig into this deeper on my own when I find the time. A few questions though

  1. In your opinion do you think that this is worse than not having PR and just doing single member Score which has no free riding?
  2. Is this a different thing than free riding since normally free riding is when you vote less for somebody in the hope of somebody else voting for them anyway. I guess this is “Vote Management” which would be strategy at the party level. MMP would not be susceptible to it but has free riding.
  3. Is there a good way to quantify this into a metric? Maybe the minimum size of controlled votes needed to get an extra seat
  4. If there is such a metric how does my system compare to RRV or STV?

Practically speaking, considering that both sides can engage in the strategy, is this really something to worry about? It’s also worth pointing out that as you go further away from the knife’s edge balance of 49-51, the less likely this is.

I don’t entirely trust single member districts due to gerrymandering, and even if the districts are drawn in good faith, I still anticipate that they will yield some distortion of public opinion in the legislature. Running simulations of PR vs Single Member Districts (for, say, a 5 member council) in the Wolf committee might be worth considering. Checking for the possibility of different kinds of strategic exploitation seems difficult, though, since there may even be strategies that we are unaware of. Perhaps machine learning could be used for this?

In section 6.1 of the Schulze paper I linked to, he argues that vote management is essentially large scale Hylland Free Riding. He gives the following STV election as an example:

10 voters a>b>c
35 voters a>c>b
25 voters b>c>a
30 voters c>b>a
In example 1, the winners are the candidates a and c. However, when the candidates a and b run a vote management strategy against candidate c and ask their supporters to vote preferably for candidate b then this example looks as follows:
10 voters b>a>c
35 voters a>c>b
25 voters b>c>a
30 voters c>b>a
Now, the winners are the candidates a and b. The fact that vote management is possible although only 3 candidates are running for 2 seats so that no elimination of candidates and, therefore, also no exhaustion of ballots occur demonstrates that none of these properties can be that property that is misused in a vote management strategy. This example demonstrates that also (1) the special rules to transfer surpluses or (2) the violation of monotonicity cannot be that property of STV methods that is misused in a vote management strategy.

That varies from election to election, so it would be difficult. Schulze said in his paper that his STV method minimized Hylland Free Riding so that it was only vulnerable in situations where this vulnerability was necessary to pass Droop Proportionality. Unfortunately, I do not know what such a criterion would look like for the PR criteria we use for score methods. For example, we could define PR as “if k Hare Quotas of voters score a set of at least k candidates max and all other candidates min, at least k of the max scored candidates should be elected.” Defining a maximal vulnerability criterion is not as simple as saying “suppose a candidate C would be elected regardless of the score a set of voters give to C, if no voters outside this set change the scores they give to C. Suppose that these voters change their scores for C in some way. Then the winner set must not change unless this would violate PR,” because this criterion is still not compatible with PR and Pareto. In the following Approval-PR election with 3 winners:
10 AD
10 BD
10 CD
No winner set outright violates PR, but Pareto requires that D be elected. If the first group of voters removes their approval of D, Pareto still requires that D be elected. PR requires that A be elected. Since the first group of voters were unnecessary for electing D, and electing A and either of the other candidates would not violate PR if D is approved, A must be elected in the original case by the “Maximal resistance” criterion. But B and C must also be elected for similar reasons. Thus the maximal resistance criterion is incompatible with PR and Pareto.

STV is probably more vulnerable to free riding than either your version of RRV or Warren Smith’s, Asking for different groups of your party to bullet vote for various assigned in a score-PR election is risky, since if you overestimate the “effective quota” or underestimate your support, the extra bullet votes will be completely wasted and you will overpay for your seat. If you underestimate the “effective quota” or overestimate your support, you may spread your voters too thin. In STV, if you do this, the votes can be salvaged: if you overestimate the quota or underestimate your support, you will only pay a fair price for your seat, and the rest of the vote transfers. If you underestimate the quota or overestimate your support, then some of your candidates will be eliminated and their votes will transfer to your other candidates.
Then again, since the effective number of votes needed to force election will be no larger than the Droop Quota, there will be a guaranteed window between the Hare Quota that a party would pay to elect candidates if they did no vote management, and the “effective quota”, parties may still deem it worth the risk, especially if their opponents are doing it, and they fear being “cheated” out of a seat.

In the first example, Party A’s strategy takes 3 of 5 seats until their support falls to 45% plus 3 votes. In the second example, when an eleventh of the electorate votes only for irrelevant candidates, they’d need to do better than 42% of the two party vote (38.2% overall) plus 3 votes.

Also, PR has multiple knife’s edges.

Does Parker’s enhancement (mostly) address this problem? I feel that in most Score PR elections, there would be more intermediate scores and showing some support for multiple candidates, and the fact that Parker’s enhancement (I’ll call it least voters-Hare quota of points or LVHQP :stuck_out_tongue:) is always looking for a Hare quota of points from the most committed voters, rather than just any of them, means that voters will feel more comfortable being honest and spreading scores around after maxing their favorite, defeating this issue. After all, it seems you need quite a few people to one-sidedly buy into this strategy for it to have strong effect.

Here is another example of vote management that is problematic because it suggests that party voters who support independent candidates can become a liability to their party’s vote management campaign. There are 5 seats, and party A leads party B 51% to 45%. The remaining 4% will back an independent campaign. Both parties run 3 candidates and evenly divide their voters among the candidates: the party A baliwicks each contain 17% of the vote, and the party B baliwicks each contain 15%. The independent is not participating in any vote management scheme, and will ask for votes from anyone willing to support them. If the independent cannot get any approvals beyond the 4%, party A wins 3 seats and party B wins 2. But the independent primarily appeals to A voters, and in a way uncorrelated with their candidate assignment: 5% out of 17% in each baliwick approve the independent in addition to their assigned candidate. So the ballots are:
12 A1
5 A1 I
12 A2
5 A2 I
12 A3
5 A3 I
15 B1
15 B2
15 B3
4 I
The independent has the highest overall score, with 19 approvals, and is elected first. Since the Hare Quota is 20, all ballots that support the independent are spent. So the second round vote is:
12 A1
12 A2
12 A3
15 B1
15 B2
15 B3
Party B wins 3 seats and a council majority.

What are the odds these voters so accurately toe the party line for their party’s candidates, but the party issues no advisory against voting for the independent?

Getting a droop quota worth of people to vote agaist their true feelings is not exactly easy.

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SIMPLER

But if that is not an option, here is another idea: What if votes are reweighted taking into account the candidate’s popularity? For example, if 33% of people approve the first winner X then their votes are deweighted by 1/2 as usual, but if 75% approved X, then they are deweighted by 1/2 * (100 - 75) / (100 - 33.3) or 0.1875 (I got the 33.3 from assuming this is a 3-district).

EDIT: Just to be super clear, those voters would have a weight of 0.8125 in the second case.

This could be the magic factor boosting cardinal PR over ordinal PR: its ability to naturally select for utilitarian-style winners. I suppose an equivalent in ordinal methods could be reducing the deweighting the closer a given candidate is to being a Condorcet winner, or in rare cases, having an unnaturally high number of 1st/2nd preference votes.

The party might well issue an advisory against voting for the independent. The problem is that if voters prefer the independent to their party’s candidates, but supporting them is a strategic mistake (e.g. a voter who most preferred the independent, but prefered party A to B) then you wind up with 2 party domination. Party A could have avoided giving B a majority by adjusting its division of voters into baliwicks so that one contains the party and independent supporters, but the party might also decide not to in order to prevent their voters from supporting the independent. It depends on whether they are willing to play chicken with their voters. They might hope that announcing their division early might prevent independent candidacies from getting off of the ground.

Do you subscribe to the theory that voters will vote honestly if near-guaranteed an acceptable result? To me, it seems very unrealistic to expect a majority of voters to strongly follow suggested divisions by the party.

But when the margin between the two major parties is thin enough, the result is not guaranteed: I provided examples where one party can use vote management to win a majority of seats, even if they win fewer votes than their opponent. The larger party can counter the strategy by also using vote management. So both parties have an incentive to run vote management strategies, since without them, they are essentially conceding the majority to their opponents.

The Schulze paper gives examples of STV elections where a party has successfully used vote management to win additional seats, so it has happened before. Furthermore, the concept of wasted votes leading to undesirable outcomes is one that voters are already familiar with, so even if voters do not understand the strategy that their preferred party is proposing, the argument that “if you do not vote as you have been instructed, you will waste your vote and put the other party into power” is one that could get people to obey instructions. Delivering different instructions to different voters would not be difficult. They could assign each polling place to a baliwick and pass out how-to-vote cards at the polling place as well as mail them.

While standard RRV is still vulnerable to free riding, this “guess and divide” strategy is not useful when all you have is a block of loyalists who will vote as you tell them. When the block of loyalists votes maximally for all your candidates and minimally for all others, if you think you can win n seats, when you have won your n-1th, this block will contribute (Size of block*Max)/n to your final candidate, which would be the best case scenario under a division-based management strategy. I will have to look into what sorts of vote management RRV is vulnerable to.

This is a bit of a naive question, as I am already aware that PR tends to have two-faction domination with some centrists winning, but do you think that there is a way for some form of PR to deliver results that fall outside the usual two-party interpretation? That might be the best way to beat vote management. I’m thinking what NoIRV suggested for “consensus-reduced deweighting” could be one such way.