Iterated Voting

Philosophy Forums Society, Government, and Economics
1

Take an election for some governmental office. Iterated Voting is a system of proxy voting that works like this.

-Put each voter in a small group.
-Each small group discusses their qualifications and decides which of them should advance towards the office.
-The advancing members are again paired (or trio’d), and the process is repeated until there is only one voter left.

In an electorate of 300 million, this process would take less than 30 iterations for groups of two, and fewer for larger groups (log base x of 300 million, where x is the group size).

The method the groups use to choose who advances can be any of a number: they could decide by consensus, they could vote (assuming an odd number), or they could draw straws.

The system would be difficult to game, because gaming would require the collaboration of a significant part of the electorate. If the grouping were random, it would effectively require the entire electorate to participate. If the grouping were not random, it would require only a very small group, ((x/2+1)/x)^y, where x is group size and y is the number of iterations.

How representative could such an outcome be? Iterative processes are good at aggregating certain types of information, but voter preference may not be aggregated very well by them. It should be possible to come up with scenarios where the best person is eliminated in favor of the worst: two groups of majority bad voters/representatives (i.e. those who vote for bad voters/representatives or would make bad office holders) and one group of good voters/representatives (i.e. those who vote for good voters/representatives or would make good office holders) would result in the selection of a bad office holder. In the real world, would this outcome be likely?

2

I love a good scheme, but…

You would invariably end up with the preferred of the preferred, the wealthiest of the wealthy, the best friend to those with best friends. And the poor would never be represented at all, not even a little bit. And there are a variety of potential scenarios that would cause that result.

3

When are the poor represented in any kind of democracy let alone any kind of government?

4

I’m confused here, are you suggesting voters or democratic participants largely ignorant where this process is needed?

5

In majority voting in regions with direct congressional representatives.

If a city was of mostly poor people who actually had un-manipulated voting potential for a city representative for the state congress, the poor people’s collective urging would be effective in persuading the higher governance.

But if that same strategy was cascaded so as to achieve a pyramid of governance, the representatives would be voting on which of them is to represent the collection of representatives at each level. Very shortly off the ground level, the actual concerns of those poor on the bottom of authority is completely overridden by the competition of representatives among themselves and the variety of insidious manipulation scenarios. You would end up with Hillarious Trumps.

6

It seems like you’re making different assumptions for each voting system.

First, if we’re comparing an election for a single office using iterated voting vs. popular voting, it doesn’t seem that iterated voting is likely to produce a less poor-friendly office-holder (mostly because popular voting produces some pretty fucking poor-unfriendly candidates).

Second, if we’re electing district representatives e.g. for a legislature like the US House of Representatives, there’s no reason why iterated voting couldn’t select someone from a poor district who represented the concerns of her poor neighbors to the same degree as popular voting would select. If the voting took place e.g. within a household, then between neighboring households, then between neighboring blocks, etc., the representative produced should reflect the makeup of the district about as well as a popular candidate.

I agree that if, instead of intentionally lumping iterations by district, we did fully random groupings, we wouldn’t get a very representative legislature, but that seems true of popular voting as well: if each representative was picked by an equal number of individuals chosen randomly from across the population, poor and minority voters would probably be equally poorly represented. Is iterative voting likely to do worse in that respect?

And followup: if it is likely to do worse, it that because it actually represents districts better (i.e. the chosen candidate is more representative of the voting population)?

7

I was merely stating what the end results would be. If you want to compare two evils, a great many more specifics are required. What would work best for one nation would not work best for another. It depends on too many other factors.

In general voting is not the way to get the best results, although has its appropriate time and place. Voting is merely choosing the best direction by following the larger snake, or worse, the larger collection of snakes.

8

I like this idea. In any case it seems better than the electoral college.

Let’s say we start with larger groups and slowly move into smaller groups: first iteration groups of 12 people, then 9, then 6, then 5, then 4, then 3. This would leave us with about 6,600 voters.

So six iterations (counting the first stage of groups of 12) could yield the voting bloc: everyone who “survives” to be in that final group would get an equal vote. Let those people decide who is president.

The best way I think to have a selection mechanism for every iteration would be for each person in a group to get 4-5 minutes to explain who they are, what they believe, their qualifications, their level of passion for the issues and politics in general… then you have everyone in the group rank everyone in the group, including themselves, on a points based system of desirability versus undesirability. Actually I can modify this slightly: each person gets anywhere from 3 to 15 minutes to make their case, so the first iteration takes up to 3 hours, the second iteration takes up to 2.25 hours, the third iteration takes up to 1.5 hours, the fourth takes up to 1.25 hours, the fifth iteration takes up to an hour, and the last up to 45 minutes. I’ll modify it even further: out of every group at every level of iterations, the two people ranked highest get to go on to the next round.

That would go as follows:

300,000,000
50,000,000
11,111,111
3,703,703
1,481,481
704,704
493,827

So in the end we have 493,827 people who will vote for president. If I did the math correctly of course. The whole system would basically be at every level a process of elimination by popular vote. Each person in the country may not get selected to move on, but at least they got to vote for who they liked most in their groups.

9

Of course not 300 million people will realistically want to go through this process. If we assume 150 million people sign up for the process, that would yield a final voting group of around 250,000 people.

10

This kind of system would, over time, naturally break down political party polarities. I think it would move the focus from party allegiance and hating the other side, to the actual issues and ideas and to a person’s character (and yes, also to their persuasiveness, but that isn’t really a bad thing).

11

Assuming no manipulation at all (zero actual probability):
Probability of choosing the best presidential candidate per iteration:
Iteration 1: 80% - 80%
Iteration 2: 80% - 64%
Iteration 3: 80% - 51%
Iteration 4: 80% - 41%
Iteration 5: 80% - 33%
Iteration 6: 80% - 26%
Iteration 7: 80% - 21%
Iteration 8: 80% - 17%
Iteration 9: 80% - 13%
Iteration 10: 80% - 11%

Even with no voting manipulation whatsoever and given a charitable probability of people voting for what their best choice really was, with every iteration, the probability of error multiplies. With 10 iterations, 90% of the time, the wrong candidate would be chosen.

If you add the more realistic probability of voter manipulation, the probability of best choice decreases dramatically yielding the probability of having the best president available near zero. Trying to compare result that with what is currently in effect is difficult at best.

You need to decrease the probability of error, decrease the amount of voting, in order to increase the probability of making the best choice. You are striving in the wrong direction.

12

I don’t think that math tells us much. First, as you rightly note, it is difficult to compare to the current system: what’s the probability that we’ll get the best candidate? Pretty low I’d guess. If it’s 80% in a decision within a small group, shouldn’t it be significantly lower in a decision within a group of the entire voting population of ~125 million?

Second, though, I don’t know that probability of picking the best candidate tells us that much. For one thing, “best” is subjective, so people in the voting population will actually disagree about whether or not the best candidate was chosen (I’m not sure that this affects the math, though, so may be irrelevant).

For another, it is probably more important to not have a terrible candidate than to have the best possible candidate, especially when they aren’t being elected to the office of absolute dictator. A system that is 10% likely to pick the best candidate but 90% likely to pick one of the top few candidates is better than a system that is 50% likely to pick the best candidate and 50% likely to pick the worst.

In iterative voting, terrible candidates are very unlikely to advance. If a terrible candidate has a 10% chance of advancing each round, after 10 rounds she has a .1^10 = .0000000001 chance of winning. That’s pretty good.

What if we look at the distribution of a voting system: what’s the function f(x) that describes a candidate’s likelihood of being elected when x is their quality as a candidate? Then, we could select the system that has the greatest area under the curve for say the top 10% of candidates.

With a few assumptions, that value is pretty easy to calculate for iterative voting: if likelihood of advancing stays constant, and likelihood is linearly related to quality so that a candidate in the 0th percentile has likelihood of 10% and a candidate in the 99% has likelihood of 80%, then f(x)=(.7x+10)^10 (I trust James will check my math). My calc is a little rusty, but I know it’s straightforward to calculate the area under the curve from 90 to 100.

I’m not sure how you could similarly do it for our current system, but given that Trump has somewhere between 30% and 50% of winning, and, as Sam Harris notes, we’d probably be better off pulling a citizen’s name out of a hat than electing Trump, I’d bet the area under that region of the curve for our current system is lower than for iterative voting.

13

Systems like this are great on paper, but usually end up hurting peoples bottoms. How about; nature puts there, what is needed there. There is an optimum kind of individual for every task, and you cannot find that through democracy or mathematics et al. You just need the situation where merit finds its own value and worth, then politics is just something which gets in the way of that. Modern westernised societies are mostly like this already, but are hindered by politics, namely democracy and big business keep fucking about with ‘it’ and depressing the markets.

Anything big like govt or corporations are going to unbalance the natural flow and exchange of information systems, what it is and where it is, is naturally arrived at if none of that interferes.

  • good system though, …as far as they go.
14

The problem is that there is no consistent correlation between the quality of the candidate and being voted into office. The issue is almost entirely dependent upon which kind of influence is being exercised on the voters and decision makers.

Phyllo picked a fruit from the tree. What is the probability that it was an apple? There are too many relevant unknowns to make sense of the question. The same is true concerning the question of whether the best candidate (the apple) was chosen by the voters (phyllo).

To improve the system, one must examine the decision making influences. In the USA, that would be the Media and the Money. Everything is done in the dark. The voters have almost nothing to say about anything. What the voters do get to see is what the Media chooses to emphasis after all of the bartering, compromising, and choosing has already been done.

Much like that famed “Purpose of Life” question, one must decide on the ambiguous notion of good and bad leadership qualities. Get that question answered in the minds of the actual decision makers (whether voters or manipulators) and then the rest is simple intelligence mechanics (information distribution and gating). Without answering that question, talking about the quality of a candidate is like talking about the existence of the undefined God - a senseless discussion.

What kind of education is what determines what kind of leadership is appropriate and what kind is chosen. The voting scheme has very little relative influence. But with every vote, every decision, the probability of error increases. You want to decrease the probability of systemic flaw by decreasing the interdependence of each decision (parallel vs series).

Given almost identical education and opportunity to vote, a million simultaneous votes is less likely to have a flawed average outcome than ten iterated/sequential votes merely because of the probability of error issue. But in the real world, there is no similarity in education, so this point is a bit moot. The real factors involve the schemes of background, off stage decision makers and script writers. USA presidents are now merely salesmen and stage props (hence Lester Holt’s comment concerning which candidate merely appears more presidential is to be the victor).

As long as that sort of thing is going on, how the voting is done is pretty irrelevant.

15

The function of the rule of “the will of the people” is not to make good decisions, but to prevent very bad ones. A democracy allows the people to rule not because they somehow have the knowledge or ideas that will work, but simply because if the leaders ever get too out of order the people will toss them out on their asses.

Beyond that, the principle “rule of the people” is irrational in so far as a group “the people” can and must have absolutely no “ideas” whatsoever (ideas are the prerogative of individuals, or of very small and closed groups of very committed individuals), and its knowledge is incredibly limited by definition of flattening discourse to the lowest common denominator. But there is nothing wrong with this lack on the part of the people, they were never supposed to know how to govern a society anyway.

As if we would allow any other field of knowledge or action to be governed by the will of the people… industry, engineering, philosophy, psychology, mathematics… yeah, no.

16

True in the short run, but in the long run, such merely inspires greater deception methods for manipulating the populous (such as the high tech hypnotic world of today).

Good is seldom obtained by merely preventing bad. And trial-and-error takes a heavy toll.

17

I think this is basically right. Similar to what Wyld said, I see democracy as in large part a concession that we’ll never be able to define what it means to be the “best” candidate, and instead focus on the the candidate who is most representative.

The problem with identifying the “best” candidate is that people in a society will disagree about the answer. And since being be “best” candidate is based on subjective values and goals, there isn’t a truly best candidate. Representativeness as a criterion ignores discussion of what the goals and values of society should be, and just looks at whether the candidate represents some aggregation of the goals and values of individuals, as expressed through their voting.

And representativeness is an empirical question. We know, for instance, that first-past-the-post voting (which we use in the US) is less representative that systems like instant runoff voting and other ranked-choice methods, where voters don’t just pick their favorite, they rank as many candidates as the like. It’s demonstrably more representative of the voters preferences because it accounts for a larger part of their preferences.

It seems like iterative voting should account for more of voter preference than a first-past-the-post system.

James, I find it interesting that you (rightly) criticize the role of the media and of wealthy and powerful individuals, but still conclude that a system that maximizes their influence (first-past-the-post popular vote) is likely to produce less error than a system that goes a long way to eliminate that influence. Not to say that it wouldn’t be possible, but we should expect rigging 30 elections to be more difficult than rigging 1.

18

I gave you a second chance to think about that. There was always an actual best choice regardless of what anyone agrees upon. What is good or bad for a nation is not a question who might agree, although their agreement is a part of the over all equation. Obviously a bad leader could do serious damage from which the nation might not ever recover (or do you believe that Hitler was a good leader for Germany?). Companies and corporations make it even more obvious when they get a bad leader. The opinions of the employees, although relevant, certainly do not determine the qualifications of a CEO.

It’s more complicated than that. And you are conflating a “first-past-the-post” with independent voting (vs dependent, series voting).

The higher the voting pyramid that you propose, the less representative the final vote will be. The lower ranks are merely voting for competitors who try to gain the right to vote. They have to vote for a strong competitor in the upper voting game. They cannot afford to elect an actual representative. And regardless, the entire competition becomes one of manipulating every voting level. Each voting level increases the probability of choosing a worse candidate than the actual best available (again regardless of whatever anyone thought “best” meant).

There could be a thousand debates or far better means to properly distribute relevant information to the voters before they make their final vote. They could even have multiple votes just to narrow down the candidates, but votes from that same level.

It is the level of voting that makes the difference. And that means that distribution of information is critical to ensuring that the democratic system has a chance of working. I think that it was Jefferson who said the same.

19

The comparison is inapposite. CEOs can be objectively evaluated because companies have an agreed goal, i.e. to earn money for shareholders. A country does not have an agreed goal. The Pennsylvania Dutch and the Silicon Valley Strivers would surely describe the ideal nation differently.

Given an agreed goal, there is an objective best, but goals are not given, and there is disagreement. If your claim is that the purpose of life is a matter of objective fact, and by extension so is the country which best maximizes that purpose, then we have exceeded the scope of a discussion of voting systems.

Can you clarify the distinction? By first-past-the-post, I mean plurality voting, i.e. everyone gets one vote and whoever gets the most wins. Not exactly how voting in the US works, but the US is a weirdly hybrid system (actually, there’s a not-unreasonable argument that the US system is a form of iterative voting, though not the form I am presenting here). What’s the independent/dependent distinction, and how do plurality voting, ranked-choice voting, and iterative voting map on to it?

This is an accurate description and a fair criticism. However, suppose there are three people in each group, and each votes for one of the other two. Then, at each level, voters pick “Candidate A represents me better than candidate B.” That way, representation is passed up the votes.

I take your point to be essentially that more noise is passed up as well, and if so I agree and it’s a real problem for the system. But again, I’m not convinced that it does worse in practice than the current system.

True, but it also increases the probability of choosing a better candidate than the actual best worst candidate. As I argue above, if likelihood of being elected is at all influenced by candidate quality, the distribution of likely outcomes probably favors iterated voting over plurality voting (or the quasi-plurality extant systems).

Have you read anything about Jason Brennan’s recent book, ‘Against Democracy’? I haven’t had a chance to read it yet, but from the short-form descriptions I have read, the system he champions, epistocracy, is basically the idea that, rather than try to inform every voter, we should only let those who are informed vote. So we’d intentionally disenfranchise the least valuable voters. I think it’s easy to see how this would be better in theory, but doing it practice in a way that can’t be captured or gamed is not obviously possible.

I think iterative voting would actually tend towards epistocracy, since it’s likely that the top of the voting pyramid would be made up of people who are relatively intelligent and well-informed (Wyld’s version, where the goal is explicitly to narrow down the set of voters, would probably be very epistocratic).

EDIT: a word.

20

Do you agree that if literally everyone had literally the exact, exact, same education, they would all agree?

… end of discussion.

Btw, that is purist, modern-day socialism.

The highest would be made of the most clever serpents who ensured that the masses remain confused and weak.