Voting with ratings

[Kotze]

SINGLE-WINNER ELECTIONS

When you use Range Voting (that is average ratings) as a single-winner voting method, there is the common problem that people have little use for intermediate slots. Even if you don't have any idea about winning probabilities, it makes sense to only use the extreme slots, the minimum for those you like less than average, the maximum for those you like more than average.

That doesn't mean that taking average ratings is a bad method. Like with Plurality Voting, you are not under pressure to put the one you like the least above anybody. In adddition, you are not under pressure to put the one you like the most below a lesser evil, at worst you support them equally. Satisfying both criteria is very uncommon among proposed ranking methods.

(To be precise: Above paragraph is true if we look at a single election with secret voting. If we look at a series of elections with recurring candidates there can be better strategies that indeed involve putting your favourite below a lesser evil, but I don't think contriving such complicated strategies that need a lot of foresight will be a common occurence.)

So is there any point to allow voters to use more rating grades than minimum and maximum?
-We could count the ratings in a different way. Say there are five slots — great, good, neutral, bad, shite — to determine the winner we could count both the great and good rating at the same value (+1) and both the bad and shite rating at the same value (-1). So whether you rate candidate X good instead of great wouldn't make a difference to that candidate's winning probability for that election.

The additional information about usage of extreme slots would be published. Aside from their expressive value the extreme slots could also be used to affect term length or whether a candidate is allowed to run in the next election.


MULTI-WINNER ELECTIONS

If you use average ratings to elect several people, you can get a very homogenic group. If more than half the voters are fully committed to 1 current — by that I mean they always give the maximum rating to candidates of that specific current and the minimum rating to everybody else — the current (provided it slates enough candidates) will not just obtain a majority of seats, but all of them. If every voter is fully committed to a current, the biggest current can slate as many candidates as seats and get them all.

To curb a current's problem of finding the right number of candidates to run and the problem of wasting your vote by showing support for underdogs, voting for candidates that don't gain a seat shouldn't cost the voter anything, unlike with Cumulative Voting. But to make the result representative of different currents, it is important that supporting candidates that gain seats comes at a cost to their supporters.

To get proportional representation out of ratings, you can use Reweighted Range Voting (this only uses ratings between 0 and a positive number). The counting follows these steps: You elect the candidate with the highest score, then readjust the weight of ballots that supported the elected candidate. Then you use the recalculated scores to elect the next candidate, then recalculate the scores again and so on, until all seats are assigned.

If the ballots only allow the ratings 0 and 1, the recalculation mechanism works like this: The weight of your ballot's ratings get reduced to 1/2 if it supports 1 already elected candidate, it becomes 1/3 if it supports 2 already elected candidates, 1/4 for 3 candidates etc. If more ratings are allowed, the deweighting formula is this:
max rating/(max rating + ratings given to already elected candidates)

A description with an example can be found here: http://www.rangevoting.org/RRVr.html. There are also more sophisticated deweighting mechanisms possible (eg. deweighting could also take into account how broad the support for elected candidates is).

[Die Neue Zeit]

Do you intend this article to be part of a larger work on democratic theory?

[Ocean Seal]

I find a multi phase election process most appealing. Somewhat ineffective but representative of the people's will. I really haven't developed a theory but I'll present my broad approach.
All candidates start out with limited television advertising time and absolutely no corporate donations.
During the first election 4 are chosen from the pool of initial candidates.
Then a second round ensues about 1 month later.
Here two are chosen and about 2 weeks later the winner is decided in a final election.

[Kotze]

Regulating ads is very complicated, candidates having the same budget doesn't mean much when the corporate media has a favourite. This is a more elegant approach: The candidates directly meet with a random sample from society, that sample asks them questions, that sample votes.

There are 2 arguments for multiple rounds:
1. The voting method the procedure is based on does not allow much expression, so the method's results are considered too fuzzy to directly declare a winner. So that voting method is used repeatedly to disqualify the bottom performers.
-This problem can also be addressed by voting only once, but with a more expressive voting method. That's more elegant.

2. The voters don't have instantly a very informed opinion about a big group of candidates, so some pre-filtering is needed.
-Here is a conflict between having candidates who are broadly supported and having interesting debates, the former calls for taking those with the highest scores, the latter calls for computing the votes in a proportional way.

It might sound good at first to use both methods for counting the same ballots, first look at average ratings to disqualify candidates from the next electoral round, then select some among the disqualified via Reweighted Range Voting to have some interview time with the candidates. But if only those with the highest ratings qualify as candidates for the next electoral round, there is also the problem that the strongest current might slate many candidates so that there is no meaningful choice left after the first round. So rather than using top ratings for the whole pre-selection, I would use it for 2 candidates and then start the reweighting to select the other 2.

[blake 3:17]

People interested in this stuff might want to look at the Fair Vote Canada site: http://www.fairvote.ca/

FVC has done some pretty good work around electoral form. It is multi-partisan and includes a fair number of right wingers. That's part of its strength and weakness,


It is hard to get a crowd on Hey Hey Ho Ho First Past The Post Has Got To Go

[Victus Mortuum]

Electing representatives IS NOT democratic! It is inherently oligarchic and inherently subject to the manipulations of money, incumbency, and demagoguery!

"It is thought to be democratic for the offices to be assigned by lot, for them to be elected is oligarchic." - Aristotle

Only POLICY being voted on is democratic.

There is no perfect voting system. They all have significant problems, while solving others. Range and approval voting systems are subject to large tactical voting as well as failing majority, condorcet, equal-and-ranked, and later-no-harm voting criteria.

[Kotze]

I advocate assignment by lot for big boards, but I'm sceptic when it comes to getting a small group or a single person.
Range and approval voting systems are subject to large tactical voting as well as failing majority, condorcet, equal-and-ranked, and later-no-harm voting criteria.If complexity of the count wasn't an issue I would prefer the Schulze Method, but since it often is an issue I have to say it depends on the situation. If the secrecy of the vote doesn't matter or a small group votes, the Schulze Method can be used. I don't know what you mean by "equal-and-ranked" — the other stuff I understand very well (probably better than you :P). I already addressed tactical voting in the original post. Range and Approval actually satisfy the criterion that you are not under pressure to put a lesser evil over your favourite, which IRV doesn't satisfy, and this criterion is also incompatible with Condorcet. In general, with Range and Approval the pressure to invert any of your preferences is practically nil. I don't regard LNHarm as particularly important (it is also incompatible with Condorcet). When I talk with IRV advocates I usually find out that they don't understand LNHarm themselves.

[Die Neue Zeit]

Comrades, I think Kotze is trying to flesh out how to apply electoral methods as they stand now towards voting for policies. For example, how does one go beyond Yes-No referenda?

[Kotze]

USING REWEIGHTED RANGE VOTING FOR A PRIORITIZATION CHART

Had a look at ckaihatsu's prioritization chart (http://postimage.org/image/35hop84dg/). Such a chart can be used as a way of allowing minorities an opportunity to talk about an issue and to try to convince others before a majoritarian voting method is used to decide on what to do about these issues (it can also be used for allocating budgets in a way that also gives minorities some power).

The chart in that image uses Cumulative Voting, so you have a number of points to spend and results are ranked based on how many points they received. I prefer that to Range Voting aka average ratings, because with average ratings a majority (or just the biggest group when the groups have too little overlap in the proposals they support) could fill as many rank positions from the top down as it wants.

However, there's a method I'd rather use than either of these methods, the method which I described in the second half of the first post in this thread, Reweighted Range Voting. I don't want that supporting an issue that doesn't make it into the consideration phase comes at a cost to the voter, to avoid the problem of vote splitting (support getting diluted by similar proposals). Simple Range Voting and Reweighted Range Voting give you that, but not Cumulative Voting. I do want that supporting an issue that makes it into a position in the aggregate ranking reduces your influence on lower positions in the aggreagate ranking, to preserve pluralism. Cumulative Voting and Reweighted Range Voting give you that, but not simple Range Voting.

To be fair, Reweighted Range Voting doing better than Cumulative Voting requires some further assumptions. If the group that meets isn't huge, a bit of discussion among supporters of similar ideas easily curbs Cumulative Voting's vote-splitting problem. One has also to consider that doing Reweighted Range Voting by hand is a bit more annoying, but if vote collection and counting is done by a machine I clearly prefer Reweighted Range. If a computer works out the priorization ballots, it's also easily justifiable to add some more features.

Given that supporting an issue that makes it into a rank position that gets consideration has to come at a cost if we want some proportionality among the voices, voters could sometimes feel pressure to vote strategically, like this: I think proposal B is very important, but many other people think that too. I also want to support less popular proposal F and proposal B will probably make it into the consideration phase without my support anyway, so why waste voting power on it?

To curb that problem, one can add some incentives to still support proposals if it looks highly probable that they get a good place in the aggregated ranking. Talking time assigned to an issue should be given not just based on the position in the aggregate ranking, but also based on the score. When it comes to deciding how an issue is presented and who presents it, some power over that question can be given to the voters who support that issue, with more power given to those who give it more (reweighted) support. (The last feature is also somewhat trollable though, that is you can vote for the consideration of an issue in the hope of giving a deliberately idiotic "support" speech, but I think inviting this strategy is far less of a problem than what the feature tries to curb.)

Another feature could be the possibility of a voter marking sets of issues as similar. Even if you think something is important you might not want to talk about basically the same thing twice or thrice. The counting algorithm then does this: Once one of the issues you marked as similar to each other receives a position in the aggregate ranking, your support for the other issues in that set is dropped for the rest of the calculation. I also have other ideas for features.

This all might sound somewhat complicated, but Google is much more complicated than that and people use it every day. The important thing is that the interface is simple (that means having a sensible default setting, if there are many features the more obscure ones are neatly tucked away and people aren't forced to use them) and that people know where to look up the information if they want to know specific details about how it calculates stuff. It looks trivial to me. Now, having such software with some privacy protection, that's the challenge.

[Jose Gracchus]

Electing representatives IS NOT democratic! It is inherently oligarchic and inherently subject to the manipulations of money, incumbency, and demagoguery!

"It is thought to be democratic for the offices to be assigned by lot, for them to be elected is oligarchic." - Aristotle

Only POLICY being voted on is democratic.

There is no perfect voting system. They all have significant problems, while solving others. Range and approval voting systems are subject to large tactical voting as well as failing majority, condorcet, equal-and-ranked, and later-no-harm voting criteria.

God, why does every demarchist think Aristotle's word is the final one on these questions. One can literally find no defense without arguments-from-authority, and vague praise for Athens.

Athenian democracy used lottery to place magistrates, and in particular the Boule council which acted as a steering and continuing committee for the larger Assembly or Ecclessia.

Neither your nor DNZ's models provide for how to really check demarchy's weaknesses as the Athenians did with the participative assembly. Obviously an entire nation or large sample is not going to meet to hold the national jury-council to task.

[Victus Mortuum]

^^^ I've largely moved away from exclusive demarchy as a model. I support it as a form of the broader desirable potential for participatory democracy.

[Kotze]

In my first post I said that there are more sophisticated mechanisms for changing the weight of a ballot than the one described, that also take into account broadness of support, which means that if there is broader support for an elected candidate, the amount of voting power each supporter "pays" is less. IIRC such a method for approval-style ballots was first described at least about a century ago by Swedish mathematician Lars Edvard Phragmén and works like this:

Every candidate has a weight of 1 that is divided equally among all ballots approving that candidate. Unlike with Cumulative Voting, this weight is only activated as something that reduces the power of your ballot after the candidate got appended to the aggregate ranking.

Calculating is done in several steps, you assign a position in the aggregate ranking, update the information for each ballot how much of a load it has to carry, then you assign the position in the aggregate ranking below the one assigned before and so on.

You start with the first position going to the candidate that if elected causes the least load on each ballot of those who approve that candidate, the load being 1/(number of ballots approving that candidate). Long story short, that's the same winner as with normal Approval Voting, the one marked on most ballots. After that, you again look at which candidate causes the least amount of average load per supporter if elected, but now you include the load from already elected candidate(s), like this:

Suppose, there are 3 options. first option A gets the first positition in the aggregate ranking, with 1000 votes. Then, we look at support for B and C, B is supported by 700 votes and C by 600. However, 300 B voters also approve A, whereas only 100 C voters do that. So, the load on a supporter of B if B is elected is 1.3/700 and the load on a supporter of C if C is elected is 1.1/600, so C gets the second position in the aggregate ranking.

I remind you that the candidates in the above text do not have to be persons, this method could also be used to reduce the number of competing proposals on an issue or to make a popularity ranking of anything in a way that also reflects tastes different from the majority.

I believe this idea can be extended to ballots with more rating possibilities besides 0 and 1, by basically treating a voter like a set of voters under Phragmén's binary system. If the ballots have a rating range from 0 to 4, we treat each voter like 4 voters with binary ballots; if a voter gives a candidate a rating of 3, that's like 3 of the 4 binary ballots approving that candidate. The load such a virtual voter set incurs during the counting process is evenly distributed among its virtual binary ballots.

Again, this method has the feature that it doesn't cost voters anything to give a rating to a loser, since supporting a candidate only reduces your voting power after that candidate got appended to the aggregate ranking. It might be a bit annoying to count by hand, but it's really easy with a computer. Again, this method appends candidates to an aggregate ranking one at a time, so we can refine the method in such a way that you as a voter have the option to sort of program your input, meaning that you can set triggers so that depending on which candidates/candidate combinations make it into the aggregate ranking, your ratings for candidates not yet appended to the aggregate ranking can be modified according to your specifications. Given that writing out this sort of specification beforehand might be too taxing an alternative approach is to display intermediate results and to allow voters to directly modify their voting over several voting rounds with diminishing vote power.

[Kotze]

BUDGET ALLOCATION WITH KNOWN PRICES
The method I described in the last post as the more sophisticated form of using ratings with reweighting can be extended to decisions where a board allocates a budget knowing what each item to be voted on costs, here's the most simple way: Instead of giving each item a cost of 1 we just put the price there and we stop appending stuff to the aggregate ranking when the board's budget is exhausted.

Here's an (incomplete!) overview of features that can be added. The following modifications don't have to be implemented from above for all voters, instead individual voters can choose whether and how to use them.

ZOOMABLE RATINGS
The voting interface can be customized. In the basic version the ratings are binary (checkmark or no checkmark), this can be replaced with higher resolutions like 0 to 4 stars, or even something more detailled. Say the underlying rating is ratings from 0 to 1200, then a checkmark is 1200 and no checkmark is 0; the 0, 1, 2, 3, 4 stars are a rating of 0, 300, 600, 900, 1200 respectively and you can also give half-stars or use a rating from 0 to 100% or directly display the detailled rating scale from 0 to 1200. Since a computer does the counting, we can just as easily use an underlying scale from 0 to 12000000000000000.

There are many other possible features here. Because it is true that only one thing at a time gets appended to the aggregate ranking, we can add mechanisms that during that rank-appending process look at what the aggregate ranking so far is and that modify the ratings for not-yet appended stuff based on what the voter indicated to do if the aggregate ranking at that point looks like this or that.

SUPPORTING 1 OPTION OF A SET
The voter can mark several options as similar to each other, so that the voter stops supporting the other options in such a set once 1 of these gets appended to the aggregate ranking. For example, if there's a poll for the 10 best video games of all time and you want to support the game series Street Fighter and you don't want that several titles from the series appear in the aggregate ranking, you use this feature. (This feature can be extended to also allow different rating changes than changing to 0.)

Using any of the next 2 features undermines the method's property that supporting non-winning candidates comes at no cost, but strictly speaking the complete truthiness of guaranteeing that requires the somewhat unrealistic assumption that the very existence of a candidate doesn't affect how voters rate other candidates. Another aspect that was true for the method without these features and that stays true with these features used is that for any set of candidates that are treated as identical to each other by the voters, the existence of candidates in that set don't interfere with each other's chances of getting appended for as long as none of them are appended to the aggregate ranking.

SUPPORT WITHOUT DILUTION
For a voting method where stuff gets appended to an aggregate ranking 1 candidate at a time and where indicating a lower preference for a candidate can reduce the likeliness to win for a more-preferred candidate — and this applies to Reweighted Range Voting and many other methods — this problem called later-no-harm failure can be managed by marking candidates as supported without dilution, meaning that the voter's preferences for candidates outside the set get only activated after all candidates in that set got appended to the aggregate ranking. Using this feature of course means that now non-winning candidates can get in the way with finding compromises (and methods without later-no-harm failure have that problem in general), so there is a trade-off. (This feature can be extended to have more priority levels, so that your support of a lower-priority set gets only activated after all those in the sets with higher priority got appended to the aggregate ranking.)

STRETCHING RATINGS TO MIN AND MAX
This feature allows that whenever it happens that all candidates at a voter's minimum or maximum rating got appended to the aggregate ranking, all the spaces between different ratings by that voter for the remaining candidates are stretched proportionally (meaning the space ratios stay the same) to fill out the entire rating spectrum.

The last 3 mentioned features are processed in this order: First check for options marked similar by the voter to possibly drop support for some things, then check whether the voter's set of undiluted support is now empty to possibly activate support for some things, then check whether the ratings for not-yet appended stuff don't touch both minimum and maximum anymore to possibly stretch ratings to min and max.

COPYING VOTE PATTERNS
The voter can just mark some things as approved and leave it at that or try to use all the aforementioned features. However, depending on how many things there are to vote on, this might be more than a bit unwieldy. There could be the feature that recommendations by parties or other organizations are available which you can just copy and then modify if you want. There could also be a feature for showing 2 recommendations at once with differences highlighted or your draft with a recommendation superimposed over it.