SODA voting (Simple Optionally-Delegated Approval)

Simple Optionally-Delegated Approval (SODA) is a single-winner system inspired by approval voting and asset voting. It is arguably Pareto dominant over these systems (at least, as used for occasional elections), which in turn are both (separately) pareto dominant over plurality; that is, it offers only advantages, and no disadvantages, when compared to approval, occasional asset, or plurality. This makes it an excellent choice as a practical voting reform proposal, as you can easily and honestly refute any argument against it. (There are many systems which are arguably better than SODA in some way, but all are also arguably worse in some other way.)

Procedure

Essentially, you vote for any number of candidates (as with approval); but you may also decide to delegate your ballot to your favorite candidate. Top approval wins. The full procedure is:

1. Candidates publicly declare their delegation order

A) Before the election, all candidates must rank the other candidates (including declared write-ins) in order of preference. Equal rankings and truncation are allowed. The candidate's rankings are all made public. Later, in the "delegation" step, any delegation from one candidate must be consistent with that candidate's rankings. This helps reduce the possibility of corrupt vote-selling or "smoke filled rooms".

2. Voters vote delegable plurality-style votes or non-delegable approval-style votes

A) Each voter submits an approval ballot. There is some way (such as an extra write-in slot) to vote for an invalid candidate named "do not delegate".

B) Any "bullet vote" - that is, a ballot which votes for only one candidate - is considered a "delegable vote" for a candidate. These votes are tallied for each candidate. Of course, any ballots which vote for "do not delegate" or any other invalid write-in are not considered as bullet votes.

C) Approval totals for each candidate are also tallied. These preliminary results are announced, along with the number of "delegable votes" each candidate has.

D) If any candidate has an absolute majority at this point, or cannot possibly be beaten by any other candidate using the delegable votes and candidate rankings available, then they win immediately.

3. Candidates choose how to delegate their delegable votes in accordance with their delegation order

A) There is a brief period - perhaps a week - for candidates to analyse and negotiate based on these preliminary results. (Actually, the correct strategies for all candidates and the resulting winner will already be obvious. Usually, all candidates except this winner would concede as soon as preliminary results are announced. However, for the occasional candidate inclined to act irrationally in a way that matters - say, by not delegating to an ally, even though the alternative is to see an enemy elected - this interim period would give them a chance to rethink things and come into reason.)

B) All candidates, in descending order of the number of delegable votes they have, publicly delegate their votes; that is, they choose a number N, and their "delegable vote" total is added to the approval totals of their top N favorites as announced in step one. They may choose N=0 - that is, not delegate their vote to anyone. They may not choose N=(number of candidates) - that is, delegate their votes to everyone. If they declared a tie in their preferences, they must either delegate to all candidates whom they included in that tie (as well as anyone they ranked above that), or none of them. (Note: Doing this in descending order prevents a weaker candidate from making an ultimatum to a stronger candidate, and thus strengthens the strategic equilibrium of any pairwise champion there is.)

4. Highest total wins

Optional rules

Prevent sliver candidates from having kingmaker power

Optional step 2.C.ii. (applied after step 2.C above): If any candidate has less than 5% (of the total votes) as delegable votes, and is not one of the top two in total votes, then those votes are automatically delegated down their preference list as far as the Condorcet winner (considering known ballots and preference orders) among the candidates on their preference list, or, in case of elections with a cycle, as far as the second member of the Smith set (this is correct CPNE strategy for a Smith set of size 3; larger Smith sets, with over two members included in the minor candidate's preference list, are hit-by-lightning unlikely).

(Note: extending delegation as far as the Condorcet winner, instead of the candidate just before the Condorcet winner, may not be correct strategy if the Condorcet winner does not need their votes. However, by definition this will not make any practical difference if other candidates use correct strategy, and even if it did it would tend to be a socially-beneficial one. Also, the rule as stated is simpler and more decisive. Candidates with more than 5% would not need to worry about this issue. Neither should readers who don't understand this paragraph.)

This rule would help make this system more attractive to major-party politicians. But it's a principled rule, not just a sop to the major parties. Consider the "kingmaker" case: in a basically 50/50 split, some tiny party has the balance of votes, and manages to extract concessions far bigger than their base of support justifies, just in order to delegate those votes or not. That's unjust, and this rule would prevent it.

This rule is recommended if SODA is to be instituted by legislation (where politicians' support is important), and not recommended if it is to be instituted by initiative/plebiscite (where simplicity is more important).

5% is a good cutoff here; that's tens of millions of voters nationally, and enough to deserve a voice. It shouldn't be too high, because this rule is effectively taking power away from voters; that's only justified if the faction is so small that the power is not legitimate, and so it's better to err a bit on the small side if anything. But under 5% - that is, under 10% of the winning coalition - doesn't deserve kingmaker power.

More-sophisticated final win criterion

Optional alternate rule 4: it would be possible, if there were multiple candidates with an absolute majority at this point, to choose the one of them with the highest initial total. That would be equivalent to considering the delegated votes as middle-rated votes in Majority Judgment. However, this extra complication would matter so rarely that it is not worth it.

Simpler, more forgiving handling of write-in candidates

Optional change to steps 1.A and 3.B: Candidates would not rank declared write-ins. Write-in candidates could receive delegated votes from any candidate, not just one who had ranked them up-front. However, to counterbalance this advantage, write-ins would not be able to delegate votes. Voters who wished to have a backup for their write-in vote would have to do so with an explicitly approval-style ballot.

Example

Tennessee's four cities are spread throughout the state

Imagine that Tennessee is having an election on the location of its capital. The population of Tennessee is concentrated around its four major cities, which are spread throughout the state. For this example, suppose that the entire electorate lives in these four cities, and that everyone wants to live as near the capital as possible.

The candidates for the capital are:

• Memphis, the state's largest city, with 42% of the voters, but located far from the other cities
• Nashville, with 26% of the voters, near the center of Tennessee
• Knoxville, with 17% of the voters
• Chattanooga, with 15% of the voters

The preferences of the voters would be divided like this:

42% of voters (close to Memphis)	26% of voters (close to Nashville)	15% of voters (close to Chattanooga)	17% of voters (close to Knoxville)
Memphis Nashville Chattanooga Knoxville	Nashville Chattanooga Knoxville Memphis	Chattanooga Knoxville Nashville Memphis	Knoxville Chattanooga Nashville Memphis

In this simplified example, all the residents of each city agree on the rankings of all the other cities, so there would be no reason for anybody to do anything but bullet vote. Memphis has the first option to delegate, and, as the leader, decides not to. Nashville goes second; it is the pairwise champion (Condorcet winner), so it also declines to delegate any of its votes. Chatanooga and Knoxville would delegate to each other and to Nashville, to prevent Memphis from winning. Nashville would then be the winner, with 58% approval after delegation.

Chatanooga could, before the election, not include Nashville in its preference list, hoping to force Nashville to delegate to it. But in that case Memphis would delegate to Nashville to prevent Nashville from being forced to hand the election to Chatanooga, and so Nashville would win with an even larger majority. Therefore, Chatanooga will not attempt this.

Criteria Compliance

SODA satisfies monotonicity, the majority criterion, the mutual majority criterion, the independence of clones criterion. Depending on assumptions and definitions, it can pass the Condorcet loser criterion.

It does not satisfy the independence of irrelevant alternatives criterion in general, but it does if the "irrelevant alternative" is assumed to delegate votes in the same way as any candidate whose delegable votes they supplant. Similarly, it can only pass the participation and consistency criteria if it is assumed that candidate delegations do not change. These assumptions are not realistic, but they do show that the method is in some sense "close to" passing these criteria.

It fails the Condorcet criterion, although the Condorcet winner over the ranking-augmented ballots is the unique strong equilibrium winner. That is to say that, under the realistic but not inviolable assumptions that candidates are honest in their pre-election rankings (not innately, but in because dishonesty would lose them votes) and strategic in their actions, and that the voters are able to use the system to express all relevant preferences, the method would in fact pass.

Advantages

1. SODA is extremely easy for the voters; in fact, no voting system is simpler to vote. (Plurality, by restricting you to only one vote, also makes it possible to mistakenly "overvote", spoiling your ballot. There is no such way to accidentally invalidate your ballot under SODA. Also, both Plurality and Approval require a conscientious voter to consider strategy and polling status; SODA allows a simple bullet vote to still be strategically as strong as possible, regardless of the candidate standings.)
2. All the steps of SODA have a clear purpose. Instead of relying on complicated rules to give a good outcome, SODA gives simple tools to the people involved, so that a good outcome is simply the rational result.
3. There is no motivation for dishonesty from individual voters. A voter can safely vote for any candidate that they honestly agree with, without fear of that vote being wasted; or safely vote an honest approval-style ballot, if they do not agree with any candidate's preference order.
4. Any vote delegation is entirely optional. Any voter who dislikes the idea of their vote being delegated in a "smoke-filled room", need not allow that to happen.
5. SODA is far more likely to arrive at a majority result than Plurality (or even IRV). It may even be more likely to give a Condorcet winner than a Condorcet system.
6. Assuming that all voters who choose to delegate their vote agree with the declared preference order of their candidate, and assuming that approval ballots are enough to express the relevant preferences of all voters who do not cast a delegable ballot, then any pairwise champion (Condorcet winner) will be a known, strong equilibrium winner. That means that, if all candidates delegate their votes rationally, no coalition of candidates can elect anybody they all prefer to the natural winner, the candidate who could beat all others one-on-one. (This is simply due to the well-known result that a CW is a Strong Nash equilibrium winner under Approval.)
7. Leaders of minority factions would have an appropriate voice for their concerns, although power would ultimately reside with any majority coalition which exists.
8. This should be generally acceptable to current politicians, who are winners in a Plurality two-party system. Plurality-style voting still works just fine, and if most votes are for major parties, this system will cleanly allow a major party to win, in many cases without going to the delegation round (especially if the major-party candidates do not pre-announce delegation preferences, thus preventing an extorting minor party from demanding their delegated votes, or if optional rule 4A is used).

Criticism and responses

"There are other systems which are better in some ways."

This is true. Condorcet, Range Voting, and Median systems (MJ, MCA, or Bucklin) each have some claim to be the "best voting system". But SODA is the best system which has no downsides versus plurality. All those other systems require more-complicated ballots. All of them require more-complicated, or even dishonest, strategic decisions from the voter, to get the most effective vote.

So in the end, while any of the systems I mentioned would be, in my opinion, a clear net benefit versus plurality, with SODA you don't need my opinion or any qualifications like "net benefit". It is simply better, in every way.

"Spoilers are still technically possible under SODA"

This is true of any system without runoffs. In fact, systems which try too hard to make spoilers impossible, may open the possibility that a candidate who expects to lose the honest vote would trick the system into thinking the winner was a spoiler, thus beating them.

SODA, by providing perfect information, makes it likely that any true pairwise champion will be known as such, and will win.

"Allowing a candidate to delegate your vote could lead corrupt back-room deals, not the voters' will, to determine the outcome"

Simple response: if you don't want a candidate to delegate your vote, don't make your vote delegable.

Also, since candidate's delegations must accord with their pre-declared preferences, there no opportunity for strategy as long as those preferences were honestly-declared. And the preferences do not represent back-room wheeling and dealing; they are public positions. The various risks of dishonestly declaring one's preference clearly outweigh the unlikely benefits they'd give.

Simple response to a candidate who makes this argument: "He just wants the only smoke-filled room to be the one inside his skull." That is, minority factions should have a seat at the table, as long as everything is done transparently. In SODA, all vote totals, preference orders, and final delegation decisions are known; in the end, that's not a smoke-filled room, it's a transparent seat at the table, with a just degree of power which is derived from the people.

"Why go to the trouble of pre-announced rankings and a second round? Why not just have candidates pre-announce their delegated approvals?"

This sounds appealing, but would not work if two similar candidates were in a close race to see which had more first-choice votes. The system as it stands allows them to see, after the votes are counted, which of them deserves to win. That one will not delegate their votes, and the other one (of necessity) will.

In general, this system, because it provides perfect information on voting totals at the time when delegation is happening, will make strategy obvious. (The pairwise champion/Condorcet winner is a strong Nash equilibrium; and even if there are 3 or 4 candidates in the Smith set, there is still a unique Coalition Proof Nash Equilibrium). This has the paradoxical result that, as long as few voters disagree with their favored candidate's ordering (or as long as there are minor "delegator-only" candidates for every preference ordering of the majors which is held by a significant number of voters), this system will in practice be more Condorcet compliant than a Condorcet method (because strategy could confound a true Condorcet method, but delegation strategy in SODA is strongly attracted by a correct equilibrium).

Sales pitches

I'm going to abandon the neutral voice and talk as myself. If you ask around on the Elections Methods mailing list, you can find me; I've posted almost the same text below as a message there.

One of SODA's advantages that I see is that, more than any other system I can think of, it is compatible with both a two-party and a multiparty system.

While many of us are convinced that, in the long run, a multiparty system is healthier, we should not neglect the importance of a voting system being compatible with two parties. Current politicians, winners under a two-party system, are in many cases the gatekeepers of reform. Yes, that's largely a case of the fox guarding the henhouse, but it's also a fact of life.

Here are the pitches one could make. Both of those pitches are feeding on the sicknesses inherent in a two-party duopoly. But that doesn't mean that SODA would feed those sicknesses or make them worse; I'm just using those sicknesses to make an argument that I think is fully justified. Remember, SODA is fully compatible with a multiparty world; in fact, as I've argued, it is in an important sense more Condorcet compliant than a Condorcet system.

For a politician (Democrat or Republican)

So, why is SODA compatible with two parties? Here's the kind of pitch you could make to a Republican or Democrat. Although I'd definitely include less disingenuous trash talk about other good systems or about third parties or independents, I'm including it here to show the kind of arguments that you could make:

"SODA encourages most voters to vote for a single candidate, just as they do today. So an average joe, who wants to put as little thought as possible into his ballot, will still be voting for one of the major parties. With the large majority of ballots in the same two-party split as today, the minor parties will have essentially no choice but to delegate their vote to one of the majors, or relegate themselves to irrelevance. So all this will do is make it so that the Libertarians (for a Rebublican)/Greens (for a Democrat) are your allies, not spoilers.

"Any other system is more of a danger to you. You ever heard of a Condorcet Winner? No? Well, most systems try to elect a Condorcet Winner, and lemme tell you something: H. Ross Perot, that's what a Condorcet winner is. Somebody who comes up in the center, in between the two parties, and it doesn't matter how incompetent or unexperienced he is, because the Democratic voters prefer him to a Republican, and the Republican voters prefer him to a Democrat, so it doesn't matter, he could be two wheels short of a tricycle, there's still no way to beat him. Well, look at how SODA handles that. The Democrat and the Republican, they don't plan to delegate their votes, so they don't announce a preference order. And then it's pointless for the centrist, the Perot, to ask them to delegate their votes to him - they can't. So if the Perot guy wants to be in the game and delegate to someone - whoever he pre-announced before the election, if anybody - he can do that; if he wants to be just a protest candidate, he doesn't announce a delegation order up front, so he either wins or loses on his own. In the first case, he's just a minor candidate, like a Green or a Libertarian, and you don't have to worry about him any more than about them. In the second case, he's irrelevant, at worst a spoiler, just as under plurality. So either way, you're at least as well-off as you are today."

For a third-party voter

OK, maybe I went a little overboard. So here's the pitch I'd make to a third-party supporter to balance it out.

"What do you want, in the end? People like you are in a minority, and I'm sure you realize that you won't take over the world overnight. So you want a fair hearing, you want a seat at the table. Most voting systems are just selling you dreams. One day, they say, you're going to convince a majority to join your team, and on that glorious day your team's gonna be in charge. How well has that worked for Republican and Democratic voters? How much important change do you see when the pendulum swings back and forth between those two parties? Not enough. The truth is, by the time you sway a majority, your big ideas are going to be watered down - and, what's worse, you're going to have to be pretending that the watered-down version is the real thing.

"But there's another option. You can keep having big ideas, and just have a system that doesn't shut you out of the room. There are a lot, a lot of people who aren't fully satisfied with 'their' party, who are looking for another option. Take off their two-party shackles, let them safely vote for someone else, and they'll jump at the chance. And there you will be, with 10, 15, 25% of the vote. No, that won't be enough to win, but it will darn well be enough to get some respect, to get your ideas a fair hearing, get some of them tried, which is what you need in order to grow. And if the major party supposedly on 'your' side doesn't listen, you will have the power to take those votes and go home. You know and I know that major party politicians, they call themselves leaders, but what they really are is cowards. When you're sitting on a double-digit pile of votes, they will listen to you, trust me."