SODA voting (Simple Optionally-Delegated Approval)

From electowiki

Simple Optional Delegated Approval (SODA) is a single-winner system inspired by approval voting and asset voting. It is arguably Pareto dominant over plurality; that is, it offers only advantages, and no disadvantages, when compared to plurality. This makes it an excellent choice as a 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. 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. 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".
  3. 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.
  4. Approval totals for each candidate are also tallied. These preliminary results are announced, along with the number of "delegable votes" each candidate has.
  5. 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.
  6. There is a brief period - perhaps a week or two - for candidates to analyse and negotiate based on these preliminary results. (Actually, in the broad majority of cases, 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.)
  7. All candidates simultaneously delegate their votes; that is, they choose an N, and add their "delegable vote" total 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.
  8. The highest total wins.

(Optional rule 4.5: 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 to the first candidate on their approval list who has more than 5% delegable votes or more than 20% total votes. They will be further delegated to the largest sequence from their original candidate's preference order which is contained in their receiving candidate's delegations. So if they originally went to A who preferred alphabetically, then and they're passed to D who delegates to BCEGH, they'll end up approving ABCDE. This rule prevents giving excessive kingmaker power to a tiny faction. Note that all delegation is still non-exclusive, approval-style.)

(Optional alternate rule 8: 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.)

Example

Tennessee's four cities are spread throughout the state
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)
  1. Memphis
  2. Nashville
  3. Chattanooga
  4. Knoxville
  1. Nashville
  2. Chattanooga
  3. Knoxville
  4. Memphis
  1. Chattanooga
  2. Knoxville
  3. Nashville
  4. Memphis
  1. Knoxville
  2. Chattanooga
  3. Nashville
  4. 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. Nashville, the pairwise champion (Condorcet winner) would have no reason 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 threaten not to delegate its votes to Nashville, hoping to force Nashville to delegate to it. But then Memphis would delegate to Nashville to prevent this from happening, and Nashville would win with an even larger majority, so Chatanooga will not attempt this.

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. Approval requires a conscientious voter to consider strategy and polling status in approving middling candidates; SODA allows a simple bullet vote to still be strategically as strong as possible.)
  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.
  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).
  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).

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).

Technical note

How can spoilers still be possible under SODA if the CW has a known, strong equilibrium in their favor? Because it is not necessarily unique. Imagine two, similar candidates in a natural majority coalition, running against one slightly-minority candidate. One of the two majority candidates is almost certain to be the CW, but if the other similar candidate can make a credible threat to withold aproval, and the CW would rather cede to this blackmail than see the minority candidate win, then the non-CW also has a (smaller) strong equilibrium in their favor.

This situation could only arise if the second candidate could "win the game of chicken", convincing the CW to extend delegated approval to them. Since the CW has the natural advantage in this game, the non-CW could only prevail if they were known not to care very much about who won if they didn't. If voters knew this about them, then their own voters could choose to explicitly approve the CW. Thus, on the whole, it is likely that SODA would get the "right" result even in this case.

(Note that all other single-round single-winner systems suffer either from some spoiler problem or from some converse problem of teaming, which is usually worse.)

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