# Voting-like mechanisms which address size of preferences?

First, a few motivating scenarios.

1: Legislative Deadlock
=======================

A legislature consists of a split two-party system, with 50 Morlocks and 50 Eloi.

Morlocks run all the machinery which produces important goods such as clothing. They really want worker rights, such as vacation time, air conditioning, etc. Also, they enjoy eating Eloi.

Eloi really want to pass an anti-cannibalism bill. They are also mildly against passing the Morlock worker-rights bill.

For the sake of argument, let's say the Morlocks get +10 utility from worker rights, and -1 utility from the anti-cannabilism bill. Symmetrically, the Eloi get +10 from anti-cannibalism and -1 from worker rights.

If the two bills are considered separately, neither will succeed, because both only get 50% of the vote. (I'm assuming for the sake of argument that a tie is not sufficient to pass a bill.)

If the two bills were bundled together, and the legislators vote myopically (considering only the pros/cons of the bill set before them), then we can achieve the best case scenario: both measures get passed, for +9 to both sides.

However, both the Morlocks and Eloi would prefer to pass their bills *without* the "pork" of the other bill tacked on. Plausibly, both parties will coordinate to make sure the bills are only ever introduced separately, or vote against the combined bill when it is introduced. Instead, they'll each attempt to bully the other side into lesser concessions. This is especially true if the two parties hate each other; voting in favor of worker rights for Morlocks may be seen as a "betrayal" of the Eloi base, and vice versa.

From this, I draw several lessons:

A. Tit-for-tat in the legislator is not automatically bad. Before thinking about this scenario, I was thinking that deals like "I'll vote for your bill if and only if you vote for mine" were *a problem,* because they distort the vote (I was thinking that it's best if everyone votes honestly). But if the two bills are voted on one at a time, we *want* 1 Morlock and 1 Eloi to make a secret deal to vote on each other's bills! Then both measures would pass.

B. Legislation is, importantly, an iterated game rather than a series of single-shot votes. This has pros and cons. On the pro side, tit-for-tat voting strategies can improve overall outcomes. On the con side, tit-for-tat can end up in deadlock where everyone hates everyone else and won't pass each other's bills, due to perceived wrongs in the past.

C. Legislation is *combinatorial*. One bill isn't really one bill; it will typically contain a complicated combination of policies. Passing one bill at a time is basically navigating a complicated multidimensional space via binary decisions. But *how* we organize the complicated space into binary decisions will make a *huge* difference in how the legislature navigates it.

2: Oversized Minority Influence
===============================

Now consider a scenario where we add one more legislator, the Time Traveler. The Time Traveler is an independent, not a Morlock or an Eloi.

The Time Traveler can break the deadlock between the Eloi and the Morlocks by voting "yes" to both bills. However, the Time Traveler is a radical who wants something in return. Specifically, the Time Traveler wants to restore the human race to what it once was through forced interbreeding of Eloi and Morlocks, destroying the [Eloi/Morlock society as it currently exists](https://en.m.wikipedia.org/wiki/Eloi).

One radical legislator should realistically be ignored or almost ignored. Instead, the minority now has a huge influence on proceedings, because he can ask for something in exchange for his vote.

3: Undersized Minority Influence
================================

What if the Time Traveler sides with the Eloi, instead? Now, we have 51 Eloi and 50 Morlocks. So long as they can maintain party unity, the Eloi can pass whatever they want. This doesn't seem right!

Proposals
=========

1: Voting currency
------------------

Each legislative term, each legislator starts with one thousand votes. They can use these votes however they want; they might blow all 1K votes on a single big important issue, or use just one vote on each issue, or whatever. This allows strength-of-preference to be expressed, which hopefully helps pass both bills.

This stops undersized minority influence: the minority is no longer helpless. The Morlocks can let the Eloi pass their no-cannabilism bill, saving their votes. Then, they can pass their own worker-rights bill with the votes they saved up. The Eloi can't oppose the bill because (hopefully) they used up too many votes getting their own bill.

This sort of codifies tit-for-tat into a mechanism. Spending more voting power now means less later. So if an Eloi spends one more vote now, the Morlocks have 1 more vote's worth of advantage later.

Variations: the winning group might "pay" the losing group, splitting up the winning votes between the losers. Also, legislators might get a "vote allowance", perhaps getting +10 votes per week rather than getting them all in a lump sum at the beginning.

### Objection #1: legislative flip-flop.

The parties could go back and forth in power, based on who has the most votes left. First, the Eloi pass a bill banning cannibalism, exhausting half their vote supply. Then, the Morlocks use their new pseudo-majority to pass a bill which makes cannibalism legal again *and* establishes worker rights. However, they exhaust most of their votes in doing so, allowing the Eloi to pass a bill which makes cannibalism illegal again, *and* rescinds worker rights. Etc. This process could terminate when everyone runs out of votes, but it's still pretty bad.

A proposed solution: bills cannot be contradicted by bills which pass with less votes. The Eloi bill might pass initially with 25K votes from the Eloi. (Remember, the Eloi have 51K votes total, due to the Time Traveler siding with them.) Then the Morlocks would collectively need to spend half their votes to overturn it. But they don't need to: they can just pass their own bill.

The strategy here is complex. The Eloi could put a clause in their bill making worker rights illegal, so that the Morlocks *do* have to overturn the Eloi bill in order to pass worker rights. But then the Eloi could *expect* their bill to be overturned, so they'd have to spend more than 50K votes to pass it, to cement it in place. But spending this many votes gives up a lot of power.

### Objection #2: strategic bills exhaust the other party

I think the critical flaw with the vote-currency idea is that someone can introduce red-herring bills which the other party *has to* vote down, but which stand no realistic chance of passing in the first place. This exhausts the other party's votes, increasing your party's power "for free".

For example, the Morlocks might repeatedly introduce the Food Bill, under which all Eloi would be immediately exterminated for food. The Eloi don't know exactly how many votes the Morlocks will cast, so to make sure they don't get eaten, they have to spend a good number of votes against this. Eventually, the Eloi's votes will be exhausted, and the Morlocks will be free to do what they like.

Together with example #1, this shows that ***the power to decide which bills get voted on, and in which order, is critical*****.**  Whoever controls this can significantly manipulate the outcomes. Perhaps this should be a significant aspect of the mechanism design? (I won't introduce any proposals for how to handle this, but, I welcome them in the comments/answers.)

2: Quadratic Voting
-------------------

This is the same as the previous suggestion, but rather than "votes", you get "voting money". [Votes are purchased with a quadratic formula](https://en.m.wikipedia.org/wiki/Quadratic_voting), such as:

| Amount Spent | Votes Purchased |
| --- | --- |
| 1   | 1   |
| 2   | 2   |
| 4   | 3   |
| 7   | 4   |
| 11  | 5   |
| etc. |   |

Roughly, this encourages you to spread out your votes rather than blow everything on a few bills, because purchasing votes for the same bill gets increasingly expensive.

More precisely, the *hope* behind quadratic voting is that ***voters will buy votes proportionate to how much they care about an issue.*** If this were true, it would provide a nice guarantee of utilitarian outcomes. For example, in legislative deadlock scenario, we would hope that Morlocks would cast 10x as many votes in favor of working rights as they would cast against the anti-cannibalism bill; and similarly, Eloi would be willing to cast 10x as many votes in favor of anti-cannibalism as they would against worker rights. Everybody wins.

Unfortunately, this seems far from true.

### Objection #1: Quadratic voting discourages voting on losing propositions.

The idea that quadratic voting incentivises you to vote proportionately to your preferences is based on the idea that *the derivative of the quadratic formula is linear*, so the cost of one additional vote is proportional to the number of votes you've already purchased. (In the example table above, the cost of one additional vote is *precisely* the number of votes you've already purchased.) This means if you stop when cost=benefit, your number of votes represents the amount of benefit.

The problem with this argument is that the *benefit* of one additional vote is based on the chance that it tips the election in your favor. So we *shouldn't* expect your votes to be proportional to the utility of a given option. Rather, we should expect your votes to be proportional to *utility times probability*. 

This means that quadratic voting, like plurality voting, has a high incentive to *avoid voting on losing propositions*.

This doesn't create an obvious problem in the Morlock vs Eloi examples, but it can create big problems in general. 

For example, suppose the legislature has to elect a Prime Minister from amongst its members. Traditionally, Morlocks vote for the current head of the Morlock party, and Eloi vote for the current head of the Eloi party, and one of the two wins by a narrow margin. Everyone knows it's a waste of votes to consider anyone else, *purely* because everyone knows it's a waste of votes to consider anyone else. (A lot like presidential elections in the USA.)

That's bad enough -- it would be better if they could elect the moderates to Prime Minister, but it's impossible (because everyone knows it's impossible, so no one would bother to vote that way, so it's impossible in fact).

But now suppose there are two Time Travelers. Both Time Travelers are *worse for everyone* than the Morlock or Eloi party leaders. However, there's a huge amount of buzz about the Time Travelers, because they're new players. No one knows whether they're feasible candidates or not. There's a lot of discussion of the pros and cons of the two Time Traveler candidates. The Eloi suspect the Morlocks will vote Time Traveler just to spite them, and vice versa. In the end, one of the Time Travelers gets elected, because *everyone is afraid their least favorite Time Traveler will get elected* and so votes for the other; and the Time Travelers have the advantage of being able to get votes from both sides, rather than only one like the Eloi and Morlock candidates.

Note that *this can be an equilibrium:* if everyone knew the race would come down to one of the two time travelers, they wouldn't want to waste any of their votes on the more traditional candidates, even if those candidates are better in every way.

So quadratic voting can produce perverse equilibria much like we see in US elections, where few *really* like the candidates they vote for.

### Objection #2: We still have the problems from before!

In addition to this, we *still have the problems from the previous proposal,* IE the legislative flip-flop problem and the exploit where you introduce "troll" bills to get the other party to use up its votes. These are pretty bad problems!

3: Nash Voting
--------------

An [earlier post of mine](https://www.lesswrong.com/posts/TQgQN8aiieKB3mYwE/nash-score-for-voting-techniques) attempted to quantify the "strength of preferences" idea *not* by considering how much you're willing to spend votes on the current issue vs save up for the next one (which is the primary mechanism I'm considering here), but rather, by trying to quantify voter's "zero points", AKA their "BATNA" / "threat point". Basically, this quantifies how much you care about the current issue by comparing it to open revolt, ie defecting from the government. If someone is close to preferring open revolt, this means they're not getting a fair deal under the current system and their preferences should be weighted more heavily.

This has some nice theory associated with it, but the concrete proposal is not any good at all. For one thing, I provided no incentive to honestly report the BATNA. Everyone should set their BATNA high in order to make their preferences louder.

However, I haven't totally lost hope for the idea, so I wanted to mention it. Any ideas for a *realistic* voting procedure that takes BATNAs into account?

Questions
=========

1.  Any ideas for *iterated voting theory*, ie, voting theory which takes into account the iterated game rather than pretending each vote is its own isolated strategic game?
2.  Any proposals for a mechanism like quadratic voting, IE which gets people to vote proportional to their preferences, but which lacks the bad-equilibria problem?
3.  Any proposal for a mechanism similar to quadratic voting or my simpler voting-points proposal, IE which lets you transfer votes to issues you care about rather than one-vote-per-issue, but which lacks the fake-issue exploit where you can drain opponents of their votes?
4.  Can anyone propose a better version of my anti-flip-flop mechanism, ie, you need to pass something with greater-or-equal votes in order to contradict previous legislation?
5.  Any better analysis of when tit-for-tat voting is good or bad for the people overall, and mechanisms to prevent/facilitate it to get better outcomes?
6.  Similarly, any analysis of when putting "pork" (ie extra stuff) into a bill is good/bad? It's generally thought of as bad, but my motivating examples make it look good. We *want* the anti-cannabilism bill to have worker-rights "pork" added in.
7.  Relatedly, mechanisms for avoiding/encouraging pork?
8.  Any proposals for splitting up the task of introducing bills vs voting on bills, so that the legislature can't play games with which version of a bill gets introduced or which order things get voted on? How should we design a mechanism for introducing bills? Should someone else than the legislators do it?