@Jack-Waugh, I think that would be welcome.
I've been interested in voting theory since I proved Arrow's impossibility theorem in a discrete math class in college as an exercise. I did not like it then, and now, decades later, I know why.
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RE: Serial Approval Vote Election
@Jack-Waugh, Thanks for working through all these examples. I, too, had some questions about the GF vote, or the more general instructions regarding always voting for every alternative subjectively preferred over the focus. For a GF vote to be instrumental in impeding termination, the G vote total would have to be at least a strict majority (that is: F > half, because equal to half is not sufficient), and the F vote total would have to be the maximum vote count and exactly equal to the G vote total. Thus it is possible for a GF vote to hinder termination. However, in addition to G blocking termination, G is preferred by the voter over F, so G blocking theloop termination with F as the final winner is also indicating the possibility for G to be a later focus and possibly a better final outcome.
For testing purposes I wrote voter-agent code for voting to stop the loop. This strictly speaking is not part of SAVE, but it does indicate what I think voters might do. Each voter-agent has a property called indifference, which is a fraction between 0.0 and 1.0. At 0.0 the slightest difference matters, while at 1.0 the voter is totally indifferent to the alternatives. All voters start at 0.0 and increment their indifference value (1) every time the focus is a Condorcet winner (because if we cannot improve upon a Condorcet winner we will eventually accept it), and (2) whenever the focus subjectively improves after having first moved away (when the focus move away, such as when in a majority cycle, we also want to be more accepting, but only as we're coming back). These are the five basic reasons for an agent to vote for the focus:
- Ideal - the focus is close to the voter's subjective ideal alternative.
- Cluster - the best and the worst of the most recent focus alternatives are really close together.
- Top-half - the spread between the best and the worst is moderately close (3x indifference) and the focus is in the top half of that spread.
- Limited-gain - the focus is close to the upper limit to any potential future gains.
- Peak - the focus is as good or better than a focus that was followed by a movement away from the agent's idea.
All of these conditions except Peak use the indifference value. The conditions are ordered from most difficult to satisfy to the easiest to satisfy.
The reason I bring this up is because I think voters might well vote for loop termination on the off-chance they can get a better result more quickly. Which implies a vote to terminate usually does not mean "I really want to terminate now" but instead is the kinder and gentler "it is okay to terminate now". Under those circumstances, the GF vote is perfectly reasonable, and supports the possibility of termination without foregoing the chance to influence the next focus choice.
RE: Serial Approval Vote Election
Electrowiki has a common example for showing how various voting systems work. This is how SAVE would handle the example.
The setup is a vote for where to locate the Tennessee state capital. The options are the four cities of Memphis, Nashville, Chattanooga, and Knoxville. In the example, the population is limited to the four cities, with a table showing this preference profile:
|----------------+----------------+------------------+----------------| | 42% of voters | 26% of voters | 15% of voters | 17% of voters | | near Memphis | near Nashville | near Chattanooga | near Knoxville | |----------------+----------------+------------------+----------------| | 1. Memphis | 1. Nashville | 1. Chattanooga | 1. Knoxville | | 2. Nashville | 2. Chattanooga | 2. Knoxville | 2. Chattanooga | | 3. Chattanooga | 3. Knoxville | 3. Nashville | 3. Nashville | | 4. Knoxville | 4. Memphis | 4. Memphis | 4. Memphis | |----------------+----------------+------------------+----------------|
The way a SAVE procedure would work with this data would probably be something like this.
Round 0: Pre-loop, initial AV round. Voters have no reason to compromise (yet) so all voters only approve their first choice. Memphis gets 42%, Nashville gets 26%, Knoxville gets 17% and Chattanooga gets 15%. Since Memphis won the AV round, it becomes the first focus.
Round 1: Memphis is the focus. The voters near Memphis all vote to terminate the loop with Memphis as the final winner, and do not vote for any other, lesser cities. All the voters near any of the other three cities have Memphis as their last choice, so they all vote for all three of the other cities. The vote count is: 42% of the vote for loop termination with Memphis as final winner, 58% for each of Nashville, Knoxville, and Chattanooga. Result. The loop continues because 42% is not a majority. Since the focus was defeated (by all three other alternatives) the focus must change. The three-way tie under both the moderate winner rule and the history score rule is a bit unusual, but the tie-resolution rule is clear.
The tie resolution rule says the tie goes to the earliest registered alternative, but I did not establish that order. For illustration purposes, I'm just going to show what happens in each of the three cases, starting with Nashville, then Chattanooga, then Knoxville. However, only one of these paths would be taken, based on an original registration order.
- Round 2, Nashville: With Nashville as the focus, the Memphis voters still just vote for Memphis since Nashville is their second choice, giving Memphis 42% of the vote. The Nashville voters vote to terminate the loop with their 26%, but that is not a majority so the loop is not terminated. Since both Chattanooga and Knoxville are both rated above Nashville (and Memphis) both these voter groups vote for both cities, giving Chattanooga and Knoxville 32% of the vote. Since no alternative defeated Nashville, it is a Condorcet winner and continues as focus.
We pause here and switch to the Chattanooga branch:
Round 2 Chattanooga: With Chattanooga as the focus, the Memphis voters are still the only group voting for Memphis (42% again), but this time they are also voting for Nashville as better than Chattanooga focus, so Nashville gets a total of 68% of the vote. The Chattanooga voters vote to terminate the loop, but with only 15% of the vote, the loop continues. Knoxville is also not getting support from any other group so it also only gets its base support of 17%. Chattanooga has been defeated by Nashville, so the loop continues. There is only one option for the focus, so the next focus will be Nashville.
Round 3 Chattanooga: With Nashville following Chattanooga as the focus, the vote counts are the same as with the Nashville branch (just one round later). Memphis gets its 42%, Nashville votes to terminate but only gets its base 26% of the vote. Chattanooga and Knoxville each support both, so they each get 32%. Net result is continuation with Nashville remaining as the focus due to its being a Condorcet winner.
We pause here to see how Knoxville goes.
Round 2 Knoxville: With Knoxville as the focus, Memphis is voting for itself, Nashville and Chattanooga. Memphis still only gets its base of 42%, but Nashville and Chattanooga both do much better. Nashville votes for both itself and Chattanooga, and ends up with 68% of the vote. Chattanooga only votes for itself, but with support from both Memphis and Nashville, its total end up at 83%. Knoxville votes to terminate, but without other support it ends up with 17%. The loop continues. The possible choices for the next focus are Nashville with 68% and Chattanooga with 83%. The moderate winner rule picks Nashville, as closest to the desired vote share of 66.5%. The history period is: 2 (Knoxville) and 1 (Memphis), giving history scores for Nashville: (2,0,2), and Chattanooga: (2,0,2), which are identical and so do not override the moderate winner choice. So the next focus is Nashville.
Round 3 Knoxville: With Nashville following Knoxville as the focus we have the exact same situation as the other two branches. Memphis gets 42%, Nashville votes to terminate with 26%, Chattanooga and Knoxville have their mutual support group and each get 32%. The loop continues, with Nashville continuing as the focus due to its being a Condorcet winner.
At this stage in the process, things can go one of two ways. Nashville is a recognized Condorcet winner so is clearly the best alternative currently proposed. If another 24% plus one voters decide Nashville is good enough, the barest majority will terminate the loop and the capital will be in Nashville. It may not happen in a single round, and there can certainly be efforts to change voter opinions and get another outcome. But Nashville is now confirmed to be the best option among the four initial alternatives.
Yet SAVE is an iterative process, and one of the most significant opportunity iteration enables is the possibility to add to the choices. The brief for this example social choice includes the explicit statement that "everyone wants to live as near to the capital as possible." It also includes an outline map of Tennessee with the four cities marked in their relative locations. That map encodes data that could change the outcome of this social choice.
I've recreated the map and drawn three indifference curves, centered in each of Memphis, Chattanooga, and Knoxville, and each passing through Nashville. Any location inside a circle is preferred by the voters near its center over Nashville. I've placed a dot at a location that is preferred over Nashville by all three of the other groups.
The addition of location A results in the revised preference profile shown here:
|----------------+----------------+------------------+----------------| | 42% of voters | 26% of voters | 15% of voters | 17% of voters | | near Memphis | near Nashville | near Chattanooga | near Knoxville | |----------------+----------------+------------------+----------------| | 1. Memphis | 1. Nashville | 1. Chattanooga | 1. Knoxville | | 2. Location A | 2. Location A | 2. Location A | 2. Chattanooga | | 3. Nashville | 3. Chattanooga | 3. Knoxville | 3. Location A | | 4. Chattanooga | 4. Knoxville | 4. Nashville | 4. Nashville | | 5. Knoxville | 5. Memphis | 5. Memphis | 5. Memphis | |----------------+----------------+------------------+----------------|
With the addition of location A, we go back to a single flow as round 4.
Round 4 rejoined: The focus is Nashville again, but the addition of location A causes a change in the vote counts. Memphis votes for itself an A because both are better than Nashville. Nashville's vote is again 26% for loop termination. Chattanooga votes for itself, A and Knoxville. Knoxville votes for itself, Chattanooga, and A. So we have 26% for loop termination, meaning continue. Memphis gets 42%, Chattanooga gets 32%, Knoxville gets 32%, and the new location A gets 74%. As A has a majority, the focus must change, and as it is the only choice, A will be the next focus.
Round 5: With A as the focus, Memphis votes for Memphis, Nashville votes for Nashville, Chattanooga votes for Chattanooga, and Knoxville votes for Knoxville and Chattanooga. Vote counts are Memphis 46%, Nashville 26%, Chattanooga 32%, and Knoxville 17%. No votes for loop termination. A is a Condorcet winner and will remain the focus for round 6.
Since new alternatives are allowed again, we get another proposal of location B.
Revised preference profile with A and B:
|----------------+----------------+------------------+----------------| | 42% of voters | 26% of voters | 15% of voters | 17% of voters | | near Memphis | near Nashville | near Chattanooga | near Knoxville | |----------------+----------------+------------------+----------------| | 1. Memphis | 1. Nashville | 1. Chattanooga | 1. Knoxville | | 2. Location B | 2. Location B | 2. Location A | 2. Chattanooga | | 3. Location A | 3. Location A | 3. Knoxville | 3. Location A | | 4. Nashville | 4. Chattanooga | 4. Nashville | 4. Nashville | | 5. Chattanooga | 5. Knoxville | 5. Location B | 5. Location B | | 6. Knoxville | 6. Memphis | 6. Memphis | 6. Memphis | |----------------+----------------+------------------+----------------|
Round 6: Focus is A, and the new alternative at B has been proposed. Memphis supports itself and B. Nashville supports itself and B. Chattanooga supports itself. Knoxville supports itself and Chattanooga. No votes for termination (A). Memphis gets 42%. Nashville gets 26%. Chattanooga gets 32%. Knoxville gets 17%. B gets 68%, and the focus. Since B is a new focus, no new proposals are allowed.
Round 7: With B as focus, Memphis supports itself. Nashville supports itself. Chattanooga supports itself, A, Knoxville, and Nashville. Knoxville supports itself, Chattanooga, A, and Nashville. No votes for loop termination. Votes are: Memphis: 42%, Nashville: 58%, Chattanooga: 32%, Knoxville: 32%, A: 32%. The loop continues, Nashville gets the focus as the only choice. Since Nashville is a repeat, new proposals are allowed. Note that we now have a cycle: Nashville, A, B, Nashville.
This time we get a compromise proposal: Location C is the average of Nashville, A and B.
Revised preference profile with A and B:
|----------------+----------------+------------------+----------------| | 42% of voters | 26% of voters | 15% of voters | 17% of voters | | near Memphis | near Nashville | near Chattanooga | near Knoxville | |----------------+----------------+------------------+----------------| | 1. Memphis | 1. Nashville | 1. Chattanooga | 1. Knoxville | | 2. Location B | 2. Location C | 2. Location A | 2. Chattanooga | | 3. Location C | 3. Location B | 3. Knoxville | 3. Location A | | 4. Location A | 4. Location A | 4. Location C | 4. Nashville | | 5. Nashville | 5. Chattanooga | 5. Nashville | 5. Location C | | 6. Chattanooga | 6. Knoxville | 6. Location B | 6. Location B | | 7. Knoxville | 7. Memphis | 7. Memphis | 7. Memphis | |----------------+----------------+------------------+----------------|
Round 8: Nashville is again the focus, and C has been proposed. Memphis supports itself, B, C, and A. Nashville supports loop termination. Chattanooga supports itself, A, Knoxville, and C. Knoxville supports itself, Chattanooga, and A. Votes are: Memphis: 42%, loop termination (Nashville): 26%, Chattanooga: 32%, Knoxville: 32%, A: 74%, B: 42%, and C: 57%. Loop continues. Two choices for next focus. Moderate winner rule selects C. History period is: 8 (Nashville), 7 (B), and 6 (A). A was active through the whole history period, with score is (2,-18,1). C has only been active in one round, so its score is (1,0,1). The history score choice replaces the moderate winner choice, so A will be the next focus. New proposals are allowed, but none are presented.
Round 9: A is focus with no new proposals. Memphis supports itself, B, and C. Nashville supports itself, C, and B. Chattanooga supports itself. Knoxville supports itself and Chattanooga. Votes are: Memphis: 42%, Nashville: 26%, Chattanooga: 32%, Knoxville: 17%, A: no votes for loop termination, B: 68%, and C: 68%. Loop continues. Two choices for next focus, both with 68%. Moderate winner rule chooses B under the tie-breaking rules. History period is: 9 (A), 8 (Nashville), 7 (B). B was active for the whole history period with score (2,-8,1). C has only been active for two rounds so its history score of (2,0,2) counts as a tie, so B will be the next focus. New proposals are allowed, but none are presented.
Round 10: B is focus with no new proposals. Memphis supports itself. Nashville supports itself, and C. Chattanooga supports itself, A, Knoxville, C, and Nashville. Knoxville supports itself, Chattanooga, A, Nashville, and C. Vote counts are: Memphis: 42%, Nashville: 58%, Chattanooga: 32%, Knoxville: 32%, A: 32%; B: no votes for loop termination, and C: 58%. Loop continues. Two chooses for next focus, both with 58%. Moderate winner rule picks Nashville using the tie-breaking rule. History period is: 10 (B), 9 (A), 8 (Nashville). Nashville's history score is: (2,-31,1), while C's history score is (3,0,3) and fully active. The better history score overrules the moderate winner rule. C is the next focus. Since C is not a repeat, no new proposals are allowed.
Round 11: C is focus, no new proposals. Memphis supports itself and B. Nashville supports itself. Chattanooga supports itself, A, and Knoxville. Knoxville supports itself, Chattanooga, A, and Nashville. Votes are: Memphis: 42%, Nashville: 43%, Chattanooga: 32%, Knoxville: 32%, A: 32%, B: 42%, and C: no votes for termination. The loop continues with C remaining the focus as a Condorcet winner.
I've not terminated the loop because it could easily continue (see below in the region between Memphis and Chattanooga, below C). SAVE will only stop when a supermajority of the voters ask for it. The context of this example does not allow me to fully justify termination. The decision to vote for loop termination is an individual choice, and is a trade-off between the current focus alternative and the potential gain or loss of continuing.
The purpose of this example is simply to run SAVE in the same context as other voting systems to see how it compares. On the plus side, SAVE gets good results when it runs long enough, uses direct voter input to resolve majority cycles (thus handling Arrow's problems with cycles), and does so in a straightforward manner in terms of Gibbard-Satterthwaite. On the minus side, SAVE takes many more rounds.
RE: Serial Approval Vote Election
I bring here just a partial analysis of the code for now, because I am feeling a bit fatigued, and also suspecting you may want to revise.
At least two rounds of voting are required to elect anyone: the initial round, which has no focus, followed by at least one round based on a focus.
This is correct. In simulations the fastest I've seen is 4 rounds, while the slowest was around 50 rounds. The average is around 20 rounds. However, the bulk of the convergence to the center happens in around 10 rounds. The voter-agents are normally set to be slow on voting for termination.
So in summary, termination happens exactly when the focus candidate has approvals from at least half the ballots and strictly more count of approvals than any other candidate. In this case, there are no more focus rounds, the election is concluded, and the focus candidate wins the election.
Correct. For termination to occur, there must be at least majority acceptance (approval is not quite the right word), and if there are any other alternatives that are preferred over the focus by a majority, the termination must be by a super-majority. For termination, more voters must vote to accept the focus than vote for any other alternative.
Looking at a breakdown into cases:
isCondorcetWinnerwill remain at
trueafter the loop completes all zero iterations, so we will keep the same focus for the subsequent round of voting (I am not weighing in right now on whether this has anything to do with the conventional notion of "Condorcet winner" despite your naming of this variable).
- Otherwise, if we have an odd number of ballots, the code will clear
isCondorcetWinnerand take the "else", to be analyzed below.
- Otherwise, if all of the
focusOptionsreceived approvals from exactly half of the ballots,
isCondorcetWinnerremains high and so we keep the focus into the next round.
- Otherwise, we take the "else".
I use the term Condorcet winner because it seems to apply. Voters are asked if they prefer any of the non-focus alternatives over the focus F. Assuming either honesty or strategy, the number of votes for a non-focus alternative A indicates how the vote would be in a simple majority one-on-one race between A and F. If no A gets more than tieCnt votes, that means F is a Condorcet winner for this set of alternatives.
The goal of changing the focus alternative is to improve the quality of the focus, making it more likely that some future round F will be a Condorcet winner.
RE: Serial Approval Vote Election
I would expect that for a candidate to receive approvals from exactly half the ballots (in a large election) would be as rare as a polling place being struck by lightning. It seems odd that the electoral procedure would be designed to look out for such a case and treat it specially.
While I was developing SAVE, I intentionally set up electorates with even numbers of agents. In the early rounds, ties are rare. But as the focus moves toward the conceptual middle of the electorate ties and near-ties become very probable.
Just to provide a general idea of the simulation results, a SAVE run with limited agents would usually have an electorate size of 250, with 10 initial alternatives and would run for an average of 20 rounds. During the run, the number of alternatives would increase by about 60 alternatives, and 4 Condorcet winners would be found and later defeated by newly introduced alternatives. The strategy voter-agents used to create new alternatives is to split the difference between the focus and a losing alternative they prefer over the focus. The idea is to try to pick up half the margin.
RE: Serial Approval Vote Election
(This is in reply to the question about tieCnt.)
@Jack-Waugh, the code is as I intended, but I can see where there might be some confusion. The tally[lastFocusIdx] value is the number of votes for termination of the process. In early rounds that is usually a very small fraction of the electorate. The ballotCnt / 2.0 value is half of the ballots cast in a round, and when a non-focus alternative A gets that number of votes it means the electorate is equally divided between the number of people who prefer A over the focus F, and those who prefer F over A.
RE: Serial Approval Vote Election
(This is in reply to the question of the reader imagining an interaction between the people and the code.)
@Jack-Waugh, basically yes. To test the process, I have simulated electorates using spatial preferences, with varying weights on the various issues. Each voter-agent judges alternatives by the distance from their individual ideal points. That way the agents can both rank and score any proposed alternative. They can also propose new alternatives and decide when to try for something better and when to accept the current focus alternative as good enough for now.
While the framework I have for creating electorates and running simulated elections for different voting systems is reasonable for doing comparisons under controlled conditions, the voter-agents are strictly mechanical in their actions. That makes it difficult to extrapolate real voter behavior. There are far too many social interactions that come into play once we start working with choice systems with iterative input. Real voters can persuade each other and be persuaded. We can also use more sophisticated methods for proposing new alternatives, and can introduce new issues into the collective, vote-moderated discussion that SAVE enables. SAVE is a tool that may potentially help in uniting us and enabling us to be our collective best. But it can only do that if we use it. Which means a lot of input from voters, i.e. us.
RE: Serial Approval Vote Election
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RE: Serial Approval Vote Election
Thank you, @multi_system_fan, for your response. A good part of why I'm posting here (as opposed to trying to get an article published in a journal), is to get feedback on whether SAVE really could be as transformative as I think it might be. Your kudos are most welcome.
However, your critical remarks are even more welcome because I am driven to get SAVE out into the real world in active use, and so far my writing has not been up to the task. I welcome any and all question and criticisms because if I'm wrong it gives me the opportunity to correct my thinking and if I'm right but did not express myself clearly, it gives me a chance to correct my writing so the next people who read about SAVE won't stumble over my earlier lack of clarity.
So, while the tally code and logic should be up soon, I'll address your other points now.
a) The phrase "focused approval" is how I think of the process, but you are correct that it could also be thought of as a series of pairwise comparisons. The difference is a matter of perspective. If you look at the ballot as a series of questions, it is a series of pairwise comparisons.
However, if you think of the ballot as a way of eliciting voter preferences and you assume that voters could do the work of placing the alternatives in an ordered list, the term "focused approval" makes a bit more sense. Given a preference order, filling out an AV ballot is just a matter of drawing the line between what is approved and what is not approved. Once that line is drawn, every alternative above it is approved, and the rest is not.
What is happening with a focused approval vote, (and I got the idea from W.D. Smith's range voting paper from 2000), is a strategic AV ballot given a preference order and the assumption that the focus alternative is predicted to win. Under those circumstances, a strategic voter who was okay with that would set their approval threshold so as to approve the focus alternative and everything better. Similarly, a strategic voter who was not okay with the focus alternative would set their approve threshold to just exclude the focus while still voting for everything better because that would maximize the chances of a better outcome even if the voter did not really approve of some of the alternatives they were voting for.
As to changing the term, the "approval" part comes from AV and is accurate in terms of the way the ballots are aggregated. Any voting technology that can handle AV ballots can be used for SAVE, and I think AV is a very good system if you are limited to one round. I'm currently partial to the "focused" part, but I initially used "targeted approval" and have considered and rejected "front-runner approval". Another option is "strategic approval". My main objection to changing the name is changing the term in all the code and tests, but that's more friction than objection and if there's a better term now is a good time to make the change. Any suggestions?
b) The mandate round is a direct and personal response to US presidential politics and to statements made by G.W. Bush to the effect that his election (with the support of just a bit over 25% of the electorate in a low-turnout election) constituted an overwhelming mandate for all his policies, including those that were never mentioned by him in his campaign.
There are certainly elections in which the mandate round is neither needed nor desired, and I generally consider it optional. However, having it there serves two purposes. There are situations in which knowing the strength of the mandate of the final result and that of the other alternatives will make a difference in what happens after the election. For example, a mandate round will differentiate between a common ground that is unifying, and a weak compromise that still needs to be sold to the electorate. For those situations, actually measuring the mandates is important even if it doesn't change the outcome.
The other purpose is to clearly differentiate between voting for the best collective outcome (the final focus alternative) and actually supporting it. In my mind, this is important during times of social change. I might vote for a compromise I don't fully support, and then continue to work to change hearts and minds so the next time the moderate result is a little closer to my radical position. Under those circumstances, having a mandate round can be very useful. Yet even when knowing the mandates is not useful in itself, having the mandate AV round be separate from the focused rounds emphasizes the difference between finding a working compromise for the whole collective and clearly holding ones own opinions and preferences.
So yes, the mandate round is optional. But at this time I think it really should be included in the SAVE discussions, even if it isn't going to be used in all SAVE procedures.
c) In my mental models the "rest" include those alternatives I'm just not familiar with and those I only know a little about. For example, in 2007, my "rest" included both Tommy Thompson and Barak Obama. Over time, Obama left that category, while Thompson remains in it. If we widen the scope to all collective choice processes (for which SAVE is designed), we still start the process with categories of alternatives, some good, some not good, and some not yet known or considered, i.e. the rest. If we are using SAVE (or some SAVE-like system) we have the time to understand our choices, learn about other alternatives, and find or create an alternative that truly reflects our collective preferences. SAVE should also help us identify alternatives whose support is changing, providing some guidance on which of the "rest" alternatives worth further consideration.
d) I agree with you that over time our preferences do become more nuanced. I disagree with the idea of introducing more finely resolved scoring in SAVE for a few reasons. My issue with anything beyond binary choices is based on Arrow's possibility theorem for two alternatives (yes, we can choose between two alternatives), Arrow's general possibility theorem (a.k.a. Arrow's impossibility theorem, which points out majority cycles are possible when there are three or more alternatives), and the Gibbard-Satterthwaite theorem (stating any system with more than two choices is either manipulable or has a dictator).
In essence, and this deserves a longer discussion, SAVE is designed to get around the problem in AIT (majority cycles) by exposing them and giving voters choices regarding what to do about them. Those choices include both defeating the cycle by proposing an alternative that is collectively preferred over every member of the cycle thus making it irrelevant, and breaking the cycle through an explicit and overwhelming choice.
SAVE doesn't exactly get around Gibbard-Satterthwaite, but instead embraces it. SAVE is facilitating a choice from among multiple alternatives. GST declares that is manipulable. SAVE responds iteratively by proposing the focus alternative and guiding voters to vote in the one way that most strongly reflects their individual preferences. If the manipulated vote fails to select this particular focus, SAVE presents another choice: usually with another focus alternative. And again asks voters to manipulate their naive approval vote into a more sophisticated focused approval vote. The iteration continues until the manipulated vote supports the selection of the focus alternative.
SAVE goes beyond these impossibility results by embracing their truth and working with the underlying reality. But as far as I can tell, this only works with binary choices. I fear that adding multiple levels of support would cause exactly the problem you suggest and introduce unwanted tactical strategies.
Again, thank you for your kudos and critiques. Please let me know if I've answered your concerns, and more importantly if I haven't.
RE: Serial Approval Vote Election
@Jack-Waugh, I apologize for my lack of clarity. I don't think it's just you. I have two responses about the tally. Hopefully one or the other will make things clearer.
- The SAVE tally as parallel pairwise majority decisions.
The pre-iteration round is just an approval vote among the initial alternatives, with the winner becoming the first focus alternative. In each subsequent focus round the ballot input is tallied exactly like an AV round, but the vote counts are interpreted differently. For each non-focus alternative A, the vote count is considered A's vote in a majority decision between A and the focus F. If A's vote count is at least half the ballots from this round, A is a potential replacement for F (assuming there is a next round and F is not a Condorcet winner). If F's vote count is strictly more votes than any non-focus alternative and is more than half the ballots cast, F becomes the final winner. Otherwise, there will be another round and the focus rules above will be used to determine the next focus.
- The SAVE tally as a series of strategic approval vote rounds.
This interpretation of SAVE considers it just a series of AV rounds. The first AV round has no expectations of who the winner might be, so voters set individual thresholds of approval. During the iteration, the applicable focus alternative is treated as the expected winner as if it were determined by a very good poll, and voters fill out their ballots strategically, approving of all alternatives better that the focus, and approving of the focus only when they want the process to terminate. The iteration continues until the current focus both gets a majority decision and is the outright AV winner.
In both interpretations, once the SAVE winner is determined there is a final AV round with individually determined thresholds to measure the mandates for each alternative.