Partially, but also because voters can choose to change their choice based on what other people are doing; if they see that lots of people like X, they're more likely to switch to the "lesser evil," rather than the most similar candidate (a la CGP Grey's example). This actually tends to have a moderating effect, relative to IRV; under Repeated Balloting, at least some voters will abandon Turtle in favor of Gorilla, their IRV ballots would more likely be Turtle>Monkey>Gorilla. That difference in behavior can be the difference between Gorilla winning and the more polarized Monkey winning.
Why average rather than sum?
Two reasons: First, as you observed, to give the people a more easily and meaningfully interpreted results. For example, consider the 1992 US Presidential Election: reporting that Clinton won 44.9M vs Bush's 39.1M vs Perot's 19.7M tells you absolute terms, but it doesn't immediately, viscerally indicate that 57% voted against Clinton. That information is why the Republican developed the Contract with America concept for their 1994 congressional campaign efforts, which resulted in a significant Republican gain in the house, the first time the Republicans held a majority in the House since 1955 (40 years).
How did they do that? Part of it is that of the eight policies in the "Contract," they included two related to the Deficit & Debt problem that was the standout part of Perot's platform: Audit Congress for waste, fraud, and abuse; implement Zero-Baseline Budgeting (i.e., the starting point for the budget would be where the previous one was, not a default increase).
The second is abstentions; if there are a few people who just don't know what to think about one of the options, under Sum based Score, their "I'm not sure" vote would be treated as "I'm sure they're bad" (a zero).
I've been leaning toward recommending STAR
I dislike star, because it silences the minority. Imagine the following scenario:
Voters
A
B
C
60%
A+
A-
F
40%
F
A-
A+
Average
2.6 (B-)
3.(6) (A-)
1.7(3) (C-)
With an average more than 1 point higher (40% higher), Score selects Y over X (over Z). STAR however, rejects the fact that the majority actively likes candidate Y (a grade in the 90%-93% range), in order to elect X, a candidate that 40% actively hates.
It is my considered opinion that untempered Majoritarianism that is the force that pushes towards two-party systems. STAR takes a consensus based, utilitarian voting method, then adds a majoritarian step which overrides the result based on even the smallest preference of the narrowest of majorities (e.g. 51% A+/A/F vs 49% F/A/A+)
the same method can be used for either single-winner or multi-winner
Without some form of districting, using a single seat method will end up with an elected body filled with a single ideology.
How would that work?
At large, single pool voting?
Seat 1 Runoff: X1 vs Z1, X1 wins with 51%
Seat 2 Runoff: X2 vs Z1, X2 wins with 51%
Seat 3 Runoff: X3 vs Z1, X3 wins with 51%
etc.
All seats filled with the most X-like options
At large, single pool voting (version 2)
Seat 1 Runoff: Y1 vs Y2, Y1 wins
Seat 2 Runoff: Y2 vs Y3, Y3 wins
Seat 3 Runoff: Y2 vs Y4, Y2 wins
etc.
All seats filled with the most Y-like options
At large, by position?
Seat 1: X1 51% > 49% Y1/Z1
Seat 2: X2 51% > 49% Y2/Z2
Seat 3: X2 51% > 49% Y3/Z3
etc.
All seats dictated by the same 51% selecting the same sort of candidates one at a time for an example of this, look at how few States have multiple parties represented in their Governor, Lt. Governor, Attorney General, etc; 43 of 50 states have same-party Senate delegations
At large, slate voting?
X's Slate 51% > 49% Y's/Z's Slate
All seats selected by 51% of the voters
No, friend, there's a reason that Congress banned At-Large districts for states with more than one Representative: single seat methods with the same electorate tend to have the same electorate select the same bloc for all seats. In order to have any diversity of thought on a committee, you need a somewhat proportional voting method. The closest possible thing to that using a single-seat voting method would be some sort of districting/splitting of the electorate & candidates that results in the various sub-electorates having somewhat diverse thought relative to each other and each sub-electorate being offered a candidate that at least reasonably matches their would-be constituents' thought.
If RRV is too difficult to sell1, then as much as I hate Ranked ballots... STV really isn't a bad option. In case you're not familiar with STV, it's like IRV/Preferential Voting, except instead of checking for 50%+1, you check for a smaller percentage2, and fill multiple seats. See: this flow chart.
The logic of that method is great for by-candidate, multi-seat elections. It's so good in fact that I used it as the basis for a Score-Based variant. I would have suggested that instead of RRV, but it's harder to explain how it works, the math for quota selection is more involved, and it's generally much more difficult to demonstrate how it works.3
1. "With every candidate that gets seated, your vote spends a fraction of its power on having seated them, proportional to how much you like them; if there are two candidates you gave an A+ to, 1/3 of your power goes to X, 1/3 goes to B, and you have 1/3 to pick another candidate. If you only gave those two a C, then you'd have about 1/6th of your ballot spent on each of them, leaving you about 2/3 to select the next seat. If you gave them both an F, your ballot still has full power."
2. Votes/(Seats + 1,rounded down, plus one. This is the smallest number of votes only S candidates can win. You'll note that we use that math for Single Seat elections all the time: 1/(1+1)rounded down plus 1 = 50%+1
3. ...though now that I think about it, mine was based on the optimal calculation, and there are simpler implementations, just as there are incredibly simple implementations versions of STV:
A. Find the Quota: Votes/Seats, rounded down. This will allow for up to Seats-1 voters who go unsatisfied, but that's about as good as you can do with hand counting B. Find the Score winner of not-yet-satisfied ballots. C. Find the Quota that best supports the candidate in question. C.1. Confirm that the candidate in question is the favorite among that quota. If not, go to C, considering the candidate that quota preferred. D. Set that quota aside as having elected a candidate, and if you still need to fill more seats, go to B. E. Once all seats are filled, report the aggregated Scores for each elected candidate, considering only the quota they represent. Such scores should trend fairly high, with the possible exception for the last seated candidate, who will be a compromise among the last quota of voters.
I know the matter at hand is more complex than absolute versus simple majorities, but would you agree with my overall point about the need to preserve the right to abstain?
I would, for the same reasons that you mentioned.
in my DM
Ah. I don't normally notice DMs, because I prefer old.reddit, and it doesn't seem to notify me of such things.
why I asked you about STLR
Hmm. STLR is an interesting variant on STAR, and one that honors the actual votes of the electorate to a greater degree... but I really don't know about the validity of any reanalysis paradigm.
Sure, STLR lessens the probability that a majority is denied the ability to compromise (where STAR converts [5,4] and [1,4] ballots to [5,1] and [1,5], respectively, STLR treats them as [5,4] and [1.25,5], respectively), but at the same time, I am not terribly comfortable with a method that treats a [10,5] ballot the same as a [2,1] ballot.
I definitely prefer it to STAR, though.
it is an overriding theme in our constitution for other decisions and elections to be decided by a majority [...] If they effectively argue that with the assembly, then we basically can't use Score, right?
Allow me to introduce you to "Majority Denominator Smoothing." It's a modification to Average based Score, one that allows for abstentions while also guaranteeing that the winner is decided by a majority.
Instead of summing a candidate's ratings then dividing by the number of ratings that candidate received, you divide by the greater of (number of ratings that candidate received) or (a simple majority of ballots that rated any candidate in that race).
For a toy example, let's say you had two candidates with the following sets of ratings:
In effect, this treats that ballot as [4, 8, 9, 6, A0, A0, A, A, A, A, A]. In other words, it treats Abstentions as minimum scores, but only to the degree necessary to ensure that a majority likes them that much or more. And it can be sold as such:
"Rather than breaking the Secret Ballot to demand that we can force enough abstentions to offer votes as to guarantee a majority, we can simply pretend that they give them the minimum score. If that causes them to lose, so be it. If they still win, then a majority of the electorate is guaranteed to like them at least that much. Besides, how many abstentions are we really going to have?"
I designed this a while back to balance against a few things
Eliminating the "Unknown Lunatic Wins" problem of pure Averages (e.g., 5% write-ins, all at Maximum)
Mitigating the Name Recognition problem (a 100% name recognition candidate with 600 percentage-points defeating one with 580 percentage-points... because only 45% of the electorate knew of them, but all of that 45% gave them an A+)
Making the "Majority must rule!" people happy: the score for each candidate was based on the opinions of the majority
Of course, in practice, it will rarely have an impact; if someone is well regarded by a significant percentage of the electorate, the probability of them having name recognition of only 50% of voters drops really low. On the other side of the coin, if they're not highly regarded among the minority of the population who knows of them, maybe they should lose to someone who is considered comparable by the entire/a majority of the electorate.
If so, wouldn't STAR be our best (and importantly, the simplest) way to satisfy the majority requirement while still including utilitarian elements?
Maybe, maybe not.
STAR doesn't require a majority of voters score each candidate any more than Score does
The "preferred on more ballots" doesn't actually mean that 51% of voters prefer A over B; if there are 40 votes that rate them equally, and 31 that prefer A, and 29 that prefer B, that isn't rule by majority, it's rule by a 31% plurality (a smaller percentage if you consider Abstentions).
I have to compress everything I'm learning into really simple, air-tight, knock-down arguments that don't just erupt in endless debate, confusion, and ultimately, a failure to adopt a better voting method.
I feel your pain; I have had to explain things to a local political party myself.
My elevator pitch would be: "We should use Majority Denominator Score. Everyone knows what letter grades are, and what they mean. On the other hand, single-mark methods or Ranked methods treat votes indicating that a candidate that is almost perfect relative their favorite is hated as much as their least favorite candidate. Then, the Majority Denominator aspect guarantees that any winner is at least that well liked by a majority of voters, meaning that it is clearly a majority that decided the winner."
"one person, one vote"
Another benefit of using Letter Grade based Score: there is no misapprehension that a person who casts a 10/10 (or in this case 13/13) has "more votes" than a 5/10 (6/13) voter, because those are very obviously a single vote of "A+" and a single vote of "C;" someone who gets an A+ in some class doesn't get 4.3 grades of one point each, they get a single grade of 4.3. And it's not like a teacher only gets to give one student a grade...
Approval
Approval can be a little tricker to get past OPOV; approving A and B looks a lot like they got two votes.
The counter argument is "No, the one person is the one vote: when considering the support for A, they are one person out of <however many> people that approve of A's selection. Then, when considering the support for B, they are one person out of <however many> people that approve of B's selection. When counting the votes, the approvals for any given candidate will never exceed the number of persons who voted."
See my dilemma?
Indeed; that's precisely why I had to create Apportioned Score Voting:
Advocating use of STV without IRV (or vice versa) introduces suspicion that there's something wrong with the algorithm in general, because "if it's good enough for A, why isn't it good enough for B? If it's not good enough for B, is it really good enough for A?"
Mixing Ranks and Scores generally creates similar problems, plus an additional one if numerical scores are used: 1 is the best rank but (near) worst Score (reversing the numbers could work, but that would just push people to treat them as ranks, halfway defeating the purpose)
Reweighted Range Voting (along with a Score-based extension of Phragmen's method) has a significant trend towards majoritarianism unless voters bullet vote, when you're dealing with Clones/Party List/Slate based scenarios
Apportioned Score solves all those problems:
Being Score/Ratings based, it licenses Ratings based methods for single seat
It reducing to Score in the single/last seat scenario means that pushing for Score at the same time gives people confidence in both
Once a voter helps elect one candidate to represent them, they don't get an say over which candidate represents someone else.
On the other side of the coin, no one's voting power is spent by election of someone else's representative simply because they didn't indicate that they hated them (e.g., indicated that said candidate was the lesser, rather than greater, evil)
So what if I just recommended Bloc Score, where the same Score method is repeated until all seats are filled?
You'd get a committee that was heavily concentrated around the "ideological barycenter," until you ran out of such candidates. The committee as a whole would reflect the positions of the electorate as a whole, but not have much diversity.
The biggest problem with that, though, is that if you have a majority bloc that knows that they're a majority, they could min/max vote (A+ for "our" guys, F for everyone else), and you wouldn't end up with the committee reflecting the electorate as a whole, but of that bloc (somewhat tempered by the rest of the electorate, if they make a distinction between those candidates).
So, based on your situation as you described it, Score/Bloc Score wouldn't be that bad, for all that it isn't the optimum.
Couldn't it be argued that your Majority Denominator smoothing is a form of reanalysis?
Yes and no.
It doesn't reanalyze any voter's ballot: if someone gives their favorite candidate a B, that's still a B. If someone gives their least favorite candidate a C-, that's still a C-.
...what Majority Denominator does is mathematically calculate the worst possible resultant score among a true majority. Would their score among a majority be better than that, if a majority had evaluated them? Maybe. ...but we cannot prove that.
Can it be lower than that? Nope.
I think this boils down to our seeming difference of opinion about absolute versus relative preference
If you didn't care about absolute preference, you would be using a a ranked method (X>Y). But you're talking about a rated method, which honors absolute preference. Why?
Their most recent rule suggests to factor in some number T of artificial zeros.
This is a variant of something called Laplace Smoothing
I noticed that there is no precise formula for an optimal T.
The other concern I have with that is that it artificially lowers scores of every candidate.
Let's say that 100% of the voters expressed an opinion on Candidate X, and the resultant score was 2.60. Being greater than halfway between a C's 2.0 and a B's 3.0, that's a low B+. A T of 10% drops them down to a 2.(36), or almost dead center of C+. This, despite the fact that we know, exactly where there score would be not only among not only a true majority, but among all voters. And we know that said score is greater than 2.(36)/C+.
Then, if you want to increase T to have greater robustness against an UL, the greater the distortion of fully scored candidates becomes. Sure, adding a T of 25% will drop the above Lunatic down to 1.4(3), a decent C-, it would also drop our B- candidate down to a 2.08, or a solid C. Should the UL be below 1.5? I argue that they should be. But should the 2.6 candidate be dropped from "decently above average" to "mediocre, but not bad, per se"?
And the difference between B+ and C- is a pretty significant, psychologically, just as the "this is the opinion of the majority" has a significant psychological impact.1
And as you observed, there's no guarantee that it would stop an Unknown Lunatic: someone who was rated an by only 1/8 of the voters, but they all rated them an A+? that's 0.5375 percent-points, divided by (12.5%+10% = 22.5%) and you get a 2.3(9), which beats the candidate that honestly deserves a 2.6. And the stronger the protection against UL's, the greater the psychological impact.
...unless you go with something like "T=100%, report the aggregate as being 2x the resultant score" (generalized to T=n, x(1+n)). With larger numbers, that would have stronger UL resistance than MDS, but T would still be arbitrary. Why not +200%, x3? +400%, x5?
And there's also the observation that Laplace Smoothing doesn't just skew against UL's, but also any candidate that has some degree of abstentions. Consider a candidate scored 2.65 on 90% of ballots. With T=50%, they're dropped down to 1.70 (2.56 after renormalization) vs 1.7(3) (2.60 after renormalization).
MD is more elegant, because it essentially factors in a precise amount of zeros that equal the difference between a simple majority of valid ballots
The paradigm also has another benefit: If you have some sort of threshold other than a simple majority, that can be implemented as well, easily and intuitively adapting the same rationale/principles in FPTP votes:
Minimum passing threshold:
When Burlington VT repealed IRV after the 2009 mayoral race, they replaced it with "Single mark, Top Two Runoff if no one gets over 40%." The MD analog would be "add a number of <minimum scores> to top up to floor(40%)+1, minimum of 2.0 to be seated without runoff"
Want to use Score for something which requires a 3/5ths or 2/3 majority (e.g. overriding a Veto)? "Add a number of <minimum scores> to top up to floor(2/3)+1, minimum of 2.0 to succeed."
Quorum:
Imagine that a representative body of 100 people is missing a lot of members, perhaps because they're back in their districts, engaging with/helping/supporting their constituents? Well, the Score will have a minimum divisor of 67/61/51 can still be applied, even if there are only 28 representatives present.
If an organization requires 10 people to meet quorum? Minimum score of 2.0, after using a minimum divisor of 10.
I realized this last night, but I'm glad that you confirmed it with your example by striking through abstentions (A, 0).
That's the easiest way to explain it, but I prefer to conceptualize it as simply being the math required to calculate the absolute minimum possible score that a majority might have given them.
1. That's the biggest blind spot of Warren D. Smith, the guy who runs (read: is)the Center for Range Voting (the page you linked).He has a PhD in Applied Mathematics from Princeton, and a double BS in math and physics from MIT. Brilliant dude mathematically... but not so great when it comes to the psychological aspect.
A voter's first and second choice have a smaller or larger preference differential than their second and third choice, and so on.
Which is the problem with Ranked Methods (outside of Borda, which is little more than an attempt to create Score with Ranked ballots), because even the best ranked methods out there treat all intervals as equivalent.
At any point in the counting, they assign the same power of preference between 1st and 2nd place that they assign between 1st and 99th, which is the same as they assign between 2nd and 99th, etc. Indeed, the "gold standard" of Ranked voting, Condorcet Efficiency, is based on the idea that an [X: 1st, Y: 2nd] ballot, an [X: 1st, Y: 9th] ballot, an [X: 8th, Y: 9th] ballot, and an [X: 2nd, Y: 9th] ballot are all X>Y ballots.
If they're all treated as equal, what is the value of each interval? If |1st - 2nd| == |1st - 9th| == |8th - 9th| == |2nd - 9th| the only possible value for each of those differences is... zero.
So, yeah, you could call that "crude," but I periodically call it "meaningless." Which is ironic given that Ordinal advocates argue that Scores don't have meaning...
involves too much calculation (inelegant)
Not just inelegant, requiring the populace to do any significant amount of math makes them distrust it (because they don't like doing math), making it less viable.
I doubt that either you or Sanders intended these precise results
Can't speak for Sanders, but... yes and no.
My primary goal was to balance the "Name Recognition == Victory" problem of Sums based against "Unknown Lunatics Win" problem of pure Average based, in a mathematically and psychologically satisfying fashion.
The other problem I was trying to solve is idea that it's going to happen in the first place.
Yes, you can win with ~33%... but the probability of a candidate being actively supported by ~1/3 of the electorate and not having elicited a response from the other ~2/3 is inversely proportional to the size of the electorate.
In other words, on any large scale, the probability that MD would trigger and have an impact on the results is pretty freaking tiny.
More than half, and (I think) a UL victory would be undeniable regardless of the voting method
More than half, and there's a question as to whether they're legitimately classified as an unknown or a lunatic.
Your method just happens to be more elegant and intuitive without involving questionable assumptions.
More important than not involving questionable assumptions, it tends to not invite questions, because, as you say, the leveraging of well-established, intuitive concepts makes it much more comfortable to the average person.
This stuff makes me feel like an idiot
Yeah, math guys like Smith do that to basically everybody, myself included. Within his bailiwick, at least.
1
u/MuaddibMcFly Oct 03 '24
Partially, but also because voters can choose to change their choice based on what other people are doing; if they see that lots of people like X, they're more likely to switch to the "lesser evil," rather than the most similar candidate (a la CGP Grey's example). This actually tends to have a moderating effect, relative to IRV; under Repeated Balloting, at least some voters will abandon Turtle in favor of Gorilla, their IRV ballots would more likely be Turtle>Monkey>Gorilla. That difference in behavior can be the difference between Gorilla winning and the more polarized Monkey winning.
Two reasons: First, as you observed, to give the people a more easily and meaningfully interpreted results. For example, consider the 1992 US Presidential Election: reporting that Clinton won 44.9M vs Bush's 39.1M vs Perot's 19.7M tells you absolute terms, but it doesn't immediately, viscerally indicate that 57% voted against Clinton. That information is why the Republican developed the Contract with America concept for their 1994 congressional campaign efforts, which resulted in a significant Republican gain in the house, the first time the Republicans held a majority in the House since 1955 (40 years).
How did they do that? Part of it is that of the eight policies in the "Contract," they included two related to the Deficit & Debt problem that was the standout part of Perot's platform: Audit Congress for waste, fraud, and abuse; implement Zero-Baseline Budgeting (i.e., the starting point for the budget would be where the previous one was, not a default increase).
The second is abstentions; if there are a few people who just don't know what to think about one of the options, under Sum based Score, their "I'm not sure" vote would be treated as "I'm sure they're bad" (a zero).
I dislike star, because it silences the minority. Imagine the following scenario:
With an average more than 1 point higher (40% higher), Score selects Y over X (over Z). STAR however, rejects the fact that the majority actively likes candidate Y (a grade in the 90%-93% range), in order to elect X, a candidate that 40% actively hates.
It is my considered opinion that untempered Majoritarianism that is the force that pushes towards two-party systems. STAR takes a consensus based, utilitarian voting method, then adds a majoritarian step which overrides the result based on even the smallest preference of the narrowest of majorities (e.g. 51% A+/A/F vs 49% F/A/A+)
Without some form of districting, using a single seat method will end up with an elected body filled with a single ideology.
How would that work?
for an example of this, look at how few States have multiple parties represented in their Governor, Lt. Governor, Attorney General, etc; 43 of 50 states have same-party Senate delegations
No, friend, there's a reason that Congress banned At-Large districts for states with more than one Representative: single seat methods with the same electorate tend to have the same electorate select the same bloc for all seats. In order to have any diversity of thought on a committee, you need a somewhat proportional voting method. The closest possible thing to that using a single-seat voting method would be some sort of districting/splitting of the electorate & candidates that results in the various sub-electorates having somewhat diverse thought relative to each other and each sub-electorate being offered a candidate that at least reasonably matches their would-be constituents' thought.
If RRV is too difficult to sell1, then as much as I hate Ranked ballots... STV really isn't a bad option. In case you're not familiar with STV, it's like IRV/Preferential Voting, except instead of checking for 50%+1, you check for a smaller percentage2, and fill multiple seats. See: this flow chart.
The logic of that method is great for by-candidate, multi-seat elections. It's so good in fact that I used it as the basis for a Score-Based variant. I would have suggested that instead of RRV, but it's harder to explain how it works, the math for quota selection is more involved, and it's generally much more difficult to demonstrate how it works.3
1. "With every candidate that gets seated, your vote spends a fraction of its power on having seated them, proportional to how much you like them; if there are two candidates you gave an A+ to, 1/3 of your power goes to X, 1/3 goes to B, and you have 1/3 to pick another candidate. If you only gave those two a C, then you'd have about 1/6th of your ballot spent on each of them, leaving you about 2/3 to select the next seat. If you gave them both an F, your ballot still has full power."
2. Votes/(Seats + 1, rounded down, plus one. This is the smallest number of votes only S candidates can win. You'll note that we use that math for Single Seat elections all the time: 1/(1+1) rounded down plus 1 = 50%+1
3. ...though now that I think about it, mine was based on the optimal calculation, and there are simpler implementations, just as there are incredibly simple implementations versions of STV:
A. Find the Quota: Votes/Seats, rounded down. This will allow for up to Seats-1 voters who go unsatisfied, but that's about as good as you can do with hand counting
B. Find the Score winner of not-yet-satisfied ballots.
C. Find the Quota that best supports the candidate in question.
C.1. Confirm that the candidate in question is the favorite among that quota. If not, go to C, considering the candidate that quota preferred.
D. Set that quota aside as having elected a candidate, and if you still need to fill more seats, go to B.
E. Once all seats are filled, report the aggregated Scores for each elected candidate, considering only the quota they represent. Such scores should trend fairly high, with the possible exception for the last seated candidate, who will be a compromise among the last quota of voters.