Welcome to The Nonlinear Library, where we use Text-to-Speech software to convert the best writing from the Rationalist and EA communities into audio. This is: Centre for Exploratory Altruism Research (CEARCH), published by Joel Tan (CEARCH) on October 18, 2022 on The Effective Altruism Forum.

Introduction

The Centre for Exploratory Altruism Research (CEARCH) emerged from the 2022 Charity Entrepreneurship Incubation Programme. In a nutshell, we do cause prioritization research, as well as subsequent outreach to update the EA and non-EA communities on our findings.

Exploratory Altruism

The Problem

There are many potential cause areas (e.g. improving global health, or reducing pandemic risk, or addressing long-term population decline), but we may not have identified what the most impactful causes are. This is the result of a lack of systematic cause prioritization research.

EA’s three big causes (i.e. global health, animal welfare and AI risk) were not chosen by systematic research, but by historical happenstance (e.g. Peter Singer being a strong supporter of animal rights, or the Future of Humanity Institute influencing the early EA movement in Oxford).

Existing cause research is not always fully systematic; for lack of time, it does not always involve (a) searching for as many causes as possible (e.g. more than a thousand) and then (b) researching and evaluating all of them to narrow down to the top causes.

The search space for causes is vast, and existing EA research organizations agree that there is room for a new organization.

The upshot of insufficient cause prioritization research, and of not knowing the most impactful causes, is that we cannot direct our scarce resources accordingly. Consequently, global welfare is lower and the world worse off than it could be.

Our Solution

To solve this problem, CEARCH carries out:

A comprehensive search for causes.

Rigorous cause prioritization research, with (a) shallow research reviews done for all causes, (b) intermediate research reviews for more promising causes, and finally (c) deep research reviews for potential top causes.

Reasoning transparency and outreach to allow both the EA and non-EA movement to update on our findings and to support the most impactful causes available.

Our Vision

We hope to discover a Cause X every three years and significantly increase support for it.

Expected Impact

If you're interested in the expected impact of exploratory altruism, do take a look at our website (link), where we discuss our theory of change and the evidence base. Charity Entrepreneurship also has a detailed report out on exploratory altruism (link).

Team & Partners

The current team currently comprises Joel Tan, the founder (link).

However, we're looking to hire additional researchers in the near future- do reach out (link) if you're interested in working with us. Do also feel free to get in touch if you wish to discuss cause prioritization research/outreach, provide advice in general, or if you believe CEARCH can help you in any way.

Research Methodology

Research Process

Our research process is iterative:

Each cause is subject to an initial shallow research round of one week of desktop research.

If the cause's estimated cost-effectiveness is at least one magnitude greater than a GiveWell top charity, it passes to the intermediate research round of two weeks of desktop research and expert interviews.

Then, if the cause's estimated cost-effectiveness is still at least one magnitude greater than a GiveWell top charity, it passes to the deep research round of four weeks of desktop research, expert interviews and potential commissioning of surveys and quantitative modelling.

The idea behind the threshold is straightforward - research at the shallower level tends to overestimate a cause's cost-effectiveness, so if a cause doesn't appear effective early on, it's probably not going to be a better-than-GiveWell bet, let alone a Cause X magnitudes more important than our current top causes. ...

Welcome to The Nonlinear Library, where we use Text-to-Speech software to convert the best writing from the Rationalist and EA communities into audio. This is: Why Weren't Hot Air Balloons Invented Sooner?, published by Lost Futures on October 18, 2022 on LessWrong.

TL;DR

Hot air balloons certainly could have arrived at least decades earlier and there's a high chance they could have arrived centuries, possibly even millennia earlier.

Jason Crawford asks, "Why did it take so long to invent X?" The post is an invitation. It asks the reader to identify low-hanging fruit, inventions that could have been invented far earlier but weren't. Now, most technologies don't fit the bill. Not everything could have been invented long before it was. Many relied on recent advancements. The airplane only became possible once engines became powerful enough to lift them into the sky. But for other inventions such as the cotton gin or flying shuttle, neither scientific nor technological barriers seem present. To this list of mysteriously absent inventions, I'd like to propose an addition: The hot air balloon.

Ancient Balloons?

The notion of the ancient or medieval world having hot air balloons makes for exciting counterfactual history. Floating Roman military lookouts, ornate balloons arriving with Zheng He’s fleet in South Asia, balloon cartographers in the age of exploration. It’s all very eye-catching, but is it realistic?

In actual history, there were no Roman, Umayyadan, or Imperial Chinese hot air balloons. In fact, highly dubious claims of ancient South American balloons aside, no one in the classical or medieval world is known to have constructed a manned balloon. The first verified flight occurred in 1783, amid the industrial revolution. This early balloon was created by the Montgolfier brothers, French industrialists in the paper industry.

Why Manned Balloons Could Have Been Invented Sooner

Previous Inventions/Historical Precedent

Mini Hot Air Balloons

The sky lantern was invented by the Chinese by at least the 3rd century AD. Constructed from paper and a small fuel source, sky lanterns operated using the same principles as manned hot air balloons, well over a thousand years prior to the invention of the latter.

Human Flight Before Balloons

Beyond this, the concept of human flight was by no means novel to Dynastic China. Man-lifting kites were likely developed shortly before the time of the Sui Dynasty (581–618). Such kites became widespread enough throughout East Asia for the Japanese government to have prohibited them at a time.

The First Hot Air Balloon Didn’t Take Long To Invent

While Joseph-Michel Montgolfier, having created parachutes in the past, possessed preexisting knowledge of aeronautics, the brothers did not begin experimenting with balloons until the winter of 1782. By the end of the year, the duo had successfully built two prototypes, the second of which had so much lifting force they lost control of it. The prototype would proceed to float for nearly two kilometers (1.2 miles) before landing. Upon touchdown, it was ripped apart by frightened passersby. By October 1783, the first manned flight occurred, and a month later on November 21, 1783, the first untethered manned balloon flight was performed.

The Montgolfiers' Balloon Was Inefficient

The Montgolfier brothers didn’t quite understand the physics involved– they believed thick smoke was the key to keeping the bag aloft, so they burned things like straw, wool, and even old shoes to produce the densest possible smoke. Not recognizing that the heat had made the bag rise, the brothers also seem to have believed at the time that they had produced a new, previously undiscovered gas that was lighter than air.

The Montgolfier brothers created a functional hot air balloon without understanding the underlying physics. They believed that it was the smoke rather than hot air that caused the balloon to rise. Because of this, they burned materials that would produce thick smoke su...

Welcome to The Nonlinear Library, where we use Text-to-Speech software to convert the best writing from the Rationalist and EA communities into audio. This is: Open Problem in Voting Theory, published by Scott Garrabrant on October 17, 2022 on LessWrong.

In the previous post, I presented the concept of a maximal lottery-lottery as follows:

We start with a finite set of candidates C and a distribution V∈Δ(C[0,1]) on utility functions on C. Given lottery-lotteries A,B∈Δ(Δ(C)), we say that A dominates B if PA∼A,B∼B,v∼V(v(A)>v(B))≥PA∼A,B∼B,v∼V(v(B)>v(A)). A maximal lottery-lottery is an M∈Δ(Δ(C)) such that for all other L∈Δ(Δ(C)), M dominates L.

Conjecture: For any C and V, there always exists a maximal lottery-lottery.

We discussed how we can construct a powerful and elegant new voting system, if only we can guarantee that a maximal lottery-lottery exists. However it is an open problem whether or not they exist. In this post, I will discuss a few different angles of attacking this conjecture.

An Infinite Game

First, consider the following partial result:

Theorem: Let D be any nonempty finite subset of Δ(C). Then, there exists an M∈Δ(D) such that for all other L∈Δ(D), M dominates L.

Proof: Consider the following symmetric two-player zero-sum game between Alice and Bob: Alice chooses an A∈D, and Bob chooses a B∈D. Alice gets utility equal to Pv∼V(v(A)>v(B))−Pv∼V(v(B)>v(A)), and Bob gets the negative of this utility. This game must have a Nash equilibrium, and in this Nash equilibrium, Alice must play a mixed strategy M∈Δ(D). Since this is a Nash equilibrium in a symmetric zero-sum game, Alice must get at least 0 utility in expectation, no matter what L∈Δ(D) Bob plays. Alice getting at least 0 utility in expectation is exactly saying that M dominates L. □

This proof is valid (you can check the details), so why doesn't it generalize to infinite subsets D, and in particular D=Δ(C)? The problem is that games with infinitely many options need not have Nash equilibria. For example consider the game where Alice and Bob each choose a natural number, and whoever chooses the larger number wins.

Fortunately, often in cases like this, you can get past finiteness assumptions by instead using compactness assumptions, and Δ(C) is compact. Indeed, games with a compact option space and continuous utility functions always have mixed strategy equilibria.

Unfortunately, the game we constructed does not have a continuous utility function! This is easy to see, because if V assigns probability 1 to a single utility function v, if v(A)>v(B), then Alice wins and gets utility 1, but as we continuously move around A, we can discontinuously jump to the game being a tie, and then to Bob winning.

Fortunately, there are a bunch of papers analyzing situations like this. Discontinuities like this show up a bunch in auctions, which also have an infinite compact option space and discontinuous utilities, resulting from discontinuities in who wins the auction.

Unfortunately, Sam Eisenstat and I spent a while looking through a bunch of papers like this, and failed to find anything that we could apply. Several things looked like they might be able to work, but everything we tried ultimately turned out to be a dead end.

A Limit of Finite Games

The above partial result is actually pretty practically useful on its own. Even if maximal lottery-lotteries do not exist, you can always just take D=Dn to be the set of all lotteries that assign each candidate a probability that is a multiple of 1nfor some large natural number n. Because of this, practically speaking, we can use the maximal lottery-lotteries voting system today, without ever proving the conjecture!

Further, we can consider what happens as we send n to infinity. If there is an odd number of voters that each have a utility function in general position, we will always get a unique distribution on Mn∈Δ(Dn) that dominates all other distributions on Dn, and we can look at what happens to Mn as n goes to infinity. Hop...

Welcome to The Nonlinear Library, where we use Text-to-Speech software to convert the best writing from the Rationalist and EA communities into audio. This is: Decision theory does not imply that we get to have nice things, published by Nate Soares on October 18, 2022 on The AI Alignment Forum.

(Note: I wrote this with editing help from Rob and Eliezer. Eliezer's responsible for a few of the paragraphs.)

A common confusion I see in the tiny fragment of the world that knows about logical decision theory (FDT/UDT/etc.), is that people think LDT agents are genial and friendly for each other.

One recent example is Will Eden’s tweet about how maybe a molecular paperclip/squiggle maximizer would leave humanity a few stars/galaxies/whatever on game-theoretic grounds. (And that's just one example; I hear this suggestion bandied around pretty often.)

I'm pretty confident that this view is wrong (alas), and based on a misunderstanding of LDT. I shall now attempt to clear up that confusion.

To begin, a parable: the entity Omicron (Omega's little sister) fills box A with $1M and box B with $1k, and puts them both in front of an LDT agent saying "You may choose to take either one or both, and know that I have already chosen whether to fill the first box". The LDT agent takes both.

"What?" cries the CDT agent. "I thought LDT agents one-box!"

LDT agents don't cooperate because they like cooperating. They don't one-box because the name of the action starts with an 'o'. They maximize utility, using counterfactuals that assert that the world they are already in (and the observations they have already seen) can (in the right circumstances) depend (in a relevant way) on what they are later going to do.

A paperclipper cooperates with other LDT agents on a one-shot prisoner's dilemma because they get more paperclips that way. Not because it has a primitive property of cooperativeness-with-similar-beings. It needs to get the more paperclips.

If a bunch of monkeys want to build a paperclipper and have it give them nice things, the paperclipper needs to somehow expect to wind up with more paperclips than it otherwise would have gotten, as a result of trading with them.

If the monkeys instead create a paperclipper haplessly, then the paperclipper does not look upon them with the spirit of cooperation and toss them a few nice things anyway, on account of how we're all good LDT-using friends here.

It turns them into paperclips.

Because you get more paperclips that way.

That's the short version. Now, I’ll give the longer version.

A few more words about how LDT works

To set up a Newcomb's problem, it's important that the predictor does not fill the box if they predict that the agent would two-box.

It's not important that they be especially good at this — you should one-box if they're more than 50.05% accurate, if we use the standard payouts ($1M and $1k as the two prizes) and your utility is linear in money — but it is important that their action is at least minimally sensitive to your future behavior. If the predictor's actions don't have this counterfactual dependency on your behavior, then take both boxes.

Similarly, if an LDT agent is playing a one-shot prisoner's dilemma against a rock with the word “cooperate” written on it, it defects.

At least, it defects if that's all there is to the world. It's technically possible for an LDT agent to think that the real world is made 10% of cooperate-rocks and 90% opponents who cooperate in a one-shot PD iff their opponent cooperates with them and would cooperate with cooperate-rock, in which case LDT agents cooperate against cooperate-rock.

From which we learn the valuable lesson that the behavior of an LDT agent depends on the distribution of scenarios it expects to face, which means there's a subtle difference between "imagine you're playing a one-shot PD against a cooperate-rock [and that's the entire universe]" and "imagine you're playing a one-shot PD against a cooperate-rock [in a universe where you fa...

Welcome to The Nonlinear Library, where we use Text-to-Speech software to convert the best writing from the Rationalist and EA communities into audio. This is: Maximal Lottery-Lotteries, published by Scott Garrabrant on October 17, 2022 on LessWrong.

In the last post we saw how by introducing lotteries, we could resolve one of the major conflicts in voting theory, between Condorcet and consistency (while also satisfying participation and clone independence). Now, we are going to make it better. How? By adding even more lotteries!

As far as I know, unlike the previous posts, the content of this post is a new proposal by me. Everything in this post should be treated as conjecture, rather than proven.

The Proposal

Fix a finite set C of candidates, and an electorate V∈Δ(C[0,1]).

First, recall the following definition of maximal lotteries. Given lotteries A,B∈Δ(C), we say that A dominates B if Pa∼A,b∼B,v∼V(v(a)>v(b))≥Pa∼A,b∼B,v∼V(v(b)>v(a)). A maximal lottery is an M∈Δ(C) such that for all other L∈Δ(C), M dominates L.

Now for maximal lottery-lotteries. Given lottery-lotteries A,B∈Δ(Δ(C)), we say that A dominates B if PA∼A,B∼B,v∼V(v(A)>v(B))≥PA∼A,B∼B,v∼V(v(B)>v(A)). A maximal lottery-lottery is an M∈Δ(Δ(C)) such that for all other L∈Δ(Δ(C)), M dominates L.

Note that when we say v(A), since A is not a candidate, but a distribution of candidates, we mean the expected value of v(a) when a is sampled from A, and similarly for v(B). Unlike in maximal lotteries, to determine whether v(A)>v(B), we need the full information of v as a utility function (up to affine transformation), not just the preference ordering over candidates.

M is a distribution on distributions on candidates, but we need to output a distribution on candidates. Thus, we imagine sampling a distribution at random from M, and then sampling a candidate at random from that distribution. The output of the maximal lottery-lotteries voting system is the distribution that assigns each candidate the probability that they would be sampled from the above procedure.

Lottery Independence

To argue for maximal lottery-lotteries, I introduce a new criterion: lottery independence.

Given an initial set of candidates, C, we could imagine fixing any distribution over candidates P∈Δ(C), and introducing a new lottery candidate, representing P. Voters vote for the lottery candidate based on their expected utility from the lottery. Whenever the lottery candidate wins, we sample a candidate according to P.

A voting system satisfies lottery independence if introducing lottery candidates does not change the probability that any candidate is elected.

This is not a criterion that voting theorists would normally talk about, because in order to satisfy it, you both have to allow the voting system to be non-deterministic, and you have to collect utility data from the voters.

Lottery independence can be thought of as a strengthening of clone independence. Instead of introducing a clone of a single candidate, we introduce a lottery, which is like a randomized clone which clones a candidate at random after the election is over.

Maximal lottery-lotteries satisfies lottery independence. Indeed, one way to think of maximal lottery-lotteries, is first we close the set of candidates under all possible lotteries, and then we run maximal lotteries on the resulting set of candidates.

Maximal lottery-lotteries also satisfies consistency and participation, since they are just maximal lotteries over a larger set of candidates.

Lottery Condorcet Criterion

Since Condorcet, consistency, and clone independence uniquely specify Maximal lotteries, if maximal lottery-lotteries is different, it must sacrifice one of these properties. It sacrifices the Condorcet criterion.

Note that in most contexts, this is where I would stop reading. My normal first question when I see a new voting system is, "Is it Condorcet?" If the answer is no, my next follow-up questions are "How often does it correctly find the correct (Condorcet)...

Welcome to The Nonlinear Library, where we use Text-to-Speech software to convert the best writing from the Rationalist and EA communities into audio. This is: AI Safety Ideas: An Open AI Safety Research Platform, published by Apart Research on October 17, 2022 on The Effective Altruism Forum.

TLDR; We present the AI safety ideas and research platform AI Safety Ideas in open alpha. Add and explore research ideas on the website here: aisafetyideas.com.

AI Safety Ideas has been accessible for a while in an alpha state (4 months, on-and-off development) and we now publish it in open alpha to receive feedback and develop it continuously with the community of researchers and students in AI safety. All of the projects are either from public sources (e.g. AlignmentForum posts) or posted on the website itself.

The current website represents the first steps towards an accessible crowdsourced research platform for easier research collaboration and hypothesis testing.

The gap in AI safety

Research prioritization & development

Research prioritization is hard and even more so in a pre-paradigmatic field like AI safety. We can grok the highest-karma post on the AlignmentForum but is there another way?

With AI Safety Ideas, we introduce a collaborative way to prioritize and work on specific agendas together through social features. We hope this can become a scalable research platform for AI safety.

Successful examples of less systematized but similar, collaborative, online, and high quality output projects can be seen in Discord servers such as EleutherAI, CarperAI, Stability AI, and Yannic Kilcher’s Discord, in hackathons, and in competitions such as the inverse scaling competition.

Additionally, we are also missing an empirically driven impact evaluation of AI safety projects. With the next steps of development described further down, we hope to make this easier and more available while facilitating more iteration in AI safety research. Systemized hypotheses testing with bounties can help funders directly fund specific results and enables open evaluation of agendas and research projects.

Mid-career & student newcomers

Novice and entrant participation in AI safety research is mostly present in two forms at the moment: 1) Active or passive part-time course participation with a capstone project (AGISF, ML Safety) and 2) flying to London or Berkeley for three months to participate in full-time paid studies and research (MLAB, SERI MATS, PIBBSS, Refine).

Both are highly valuable but a third option seems to be missing: 3) An accessible, scalable, low time commitment, open research opportunity. Very few people work in AI safety and allowing decentralized, volunteer or bounty-driven research will allow many more to contribute to this growing field.

By allowing this flexible research opportunity, we can attract people who cannot participate in option (2) because of visa, school / life / work commitments, location, rejection, or funding while we can attract a more senior and active audience compared to option (1).

Next steps

OctReleasing and building up the user base and crowdsourced content. Create an insider build to test beta features. Apply to join the insider build here.NovImplementing hypothesis testing features: Creating hypotheses, linking ideas and hypotheses, adding negative and positive results to hypotheses. Creating an email notification system.DecCollaboration features: Contact others interested in the same idea and mentor ideas. A better commenting system with a results comment that can indicate if the project has been finished or not, what the results are, and by who was it done.JanAdding moderation features: Accepting results, moderating hypotheses, admin users. Add bounty features for the hypotheses and a simple user karma system.FebShare with ML researchers and academics in EleutherAI and CarperAI. Implement the ability to create special pages with specific private and public ideas curated for a specific purpose (title and desc...

Welcome to The Nonlinear Library, where we use Text-to-Speech software to convert the best writing from the Rationalist and EA communities into audio. This is: They gave LLMs access to physics simulators, published by ryan b on October 17, 2022 on LessWrong.

Over at Google, large language models have been plugged into physics simulators to help them share a world model with their human interlocutors, resulting in big performance gains. They call it Mind's Eye.This is how the authors describe the work:

Correct and complete understanding of properties and interactions in the physical world is not only essential to achieve human-level reasoning (Lake et al., 2017), but also fundamental to build a general-purpose embodied intelligence (Huang et al., 2022). In this work, we investigate to what extent current LMs understand the basic rules and principles of the physical world, and describe how to ground their reasoning with the aid of simulation. Our contributions are three-fold:

We propose a new multi-task physics alignment dataset, UTOPIA, whose aim is to benchmark how well current LMs can understand and reason over some basic laws of physics (§2). The dataset contains 39 sub-tasks covering six common scenes that involve understanding basic principles of physics (e.g., conservation of momentum in elastic collisions), and all the ground-truth answers are automatically generated by a physics engine. We find that current large-scale LMs are still quite limited on many basic physics-related questions (24% accuracy of GPT-3 175B in zero-shot, and 38.2% in few-shot).

We explore a paradigm that adds physics simulation to the LM reasoning pipeline (§3) to make the reasoning grounded within the physical world. Specifically, we first use a model to transform the given text-form question into rendering code, and then run the corresponding simulation on a physics engine (i.e., MuJoCo (Todorov et al., 2012)). Finally we append the simulation results to the input prompts of LMs during inference. Our method can serve as a plug-and-play framework that works with any LM and requires neither handcrafted prompts nor costly fine-tuning.

We systematically evaluate the performance of popular LMs in different sizes on UTOPIA before and after augmentation by Mind’s Eye, and compare the augmented performance with many existing approaches (§4.2). We find Mind’s Eye outperforms other methods by a large margin in both zero-shot and few-shot settings. More importantly, Mind’s Eye is also effective for small LMs, and the performance with small LMs can be on par or even outperform that of 100× larger vanilla LMs.

This seems like a direct step down the CAIS path of development.

Thanks for listening. To help us out with The Nonlinear Library or to learn more, please visit nonlinear.org.

Welcome to The Nonlinear Library, where we use Text-to-Speech software to convert the best writing from the Rationalist and EA communities into audio. This is: Be careful with (outsourcing) hiring, published by rmoehn on October 17, 2022 on The Effective Altruism Forum.

Who makes up an organization, a community? People. People do the work. People make the decisions. Choosing people well is the most important thing we do. People choice is self-reinforcing, too. Choose one bad COO and he’ll hire more bad people. Have a few bad people in an organization and nobody good will want to work there anymore. Hiring, therefore, is vital.

What do you want from a hiring process? A good hire. Crucially, no bad hire. And for those people whom you haven’t hired to be mostly happy with how things went. Because you care for them.

Sadly, you’re at risk of making a bad hire and disgruntling your other applicants if you don’t know what you’re doing. If you don’t know what you’re doing, outsourcing isn’t a solution, either, because you don’t know how to judge the actions of those you’re outsourcing to. I will demonstrate this by example of a hiring process I’ve observed as an outsider, in which the hiring firm (call them Hirely) acted in a way that would have seemed sensible to the average founder who knows little about hiring, but to me looked like blundering. Even if you don’t plan to outsource hiring, the following points are worth thinking about.

Added 2022-10-16: I won't be arguing every point fully. One commenter even wrote that I make ‘lots of general assertions without a clear explanation as to why people should believe [me]’. (I appreciate this comment.) That's because doing otherwise would have made the article ten times longer. Hiring is a wide field and I've only tilled a small patch of it myself. I encourage you to follow the links to Manager Tools podcasts/whitepapers that I've included the article. They argue many of the claims properly. I will also be glad to explain more in the comments.

This is a repurposed article with a history

(Expanded on 2022-10-16 from the last paragraph of the originally published introduction. This describes the article's history in boring detail. Feel free to skip.)

This article is strange because it's repurposed from a direct critique of the organization behind ‘Hirely’, which is a fictional name. (Please don't try to find out who is behind that name.) This is the first part of the article's history step-by-step:

I observe the hiring process in which Hirely is advising the hiring manager. (I'm also advising the hiring manager, mostly telling him to be more involved and listen to Manager Tools.)

I think Hirely is giving harmful advice.

I write this article as a direct critique.

I give the article to Hirely to react to. I tell them that I will edit it to be more general and not point the finger at them (meaning I won't out the organization by name) if they convince me that they're on a better trajectory. You may view this as being kind or you may view it as blackmail.

Hirely deliberates internally.

Hirely responds to me with the improvements they've made and are making, and asks me to deliver on my promise to edit the critique before publishing. Their response does make me think they're on a better path. (So again, please don't try to find out who they are.)

Since I'm too lazy to rewrite the whole damn article, I search and replace the organization name with ‘Hirely’, and rewrite only the introduction.

Despite this laziness, I was happy with the way it demonstrated the new main point with specificity (lwspec): If you know very little about X, you can’t safely outsource X. If X = hiring, it’s especially bad. So you better learn something about hiring.

You're already yawning, but the story isn't over. To explain all the strangenesses of this article, I have to describe the rest:

I publish the article.

It receives a lot of downvotes in addition to upvotes.

I add a prescript (opposite of postscript) asking ...

Welcome to The Nonlinear Library, where we use Text-to-Speech software to convert the best writing from the Rationalist and EA communities into audio. This is: Voting Theory Introduction, published by Scott Garrabrant on October 17, 2022 on LessWrong.

Sequence Introduction

This is the first post in a sequence in which I will propose a new voting system!

In this post, I introduce the framework and notation, and give some background on voting theory.

In the next post, I will show you the best voting system you've probably never heard of, maximal lotteries. (Seriously, it's really good.)

After that, I will make it even better, and propose a new system: maximal lottery-lotteries.

Then comes the bad news: I can't prove that maximal lottery-lotteries exist! (Or alternatively, good news: You can try to solve a cool new open problem in voting theory!)

Thanks to Jessica Taylor for first introducing me to maximal lotteries, and Sam Eisenstat for spending many hours with me trying to prove the existence of maximal lottery-lotteries.

Generalizing Voting Theory

A voting system is a function that takes in a distribution on utility functions on a set of candidates, and produces a distribution on that set of candidates.

This is not what a voting theorist will tell you a voting system is. That is because they like to make a bunch of extra assumptions:

The set of candidates is finite.

The function only uses the preorders on candidates implied by the utility functions.

The output distribution assigns probability 1 to a single candidate.

The input distribution is the uniform distribution on some finite set.

I am going to play along with some of these assumptions, but I want my types and notation to treat them as explicit assumptions, so I will use notation that will make it easy to remove these assumptions as needed.

Technically, I also make one assumption that voting theorists usually don't make. That is that the voting system is homogeneous. Homogeneous voting systems are only a function of what proportion of voters have each preference, not on the absolute number of voters that have each preference. Thus, when I said the input was a distribution on utility functions, rather than a multi-set of utility functions, I threw out the information that would have allowed for non-homogeneous voting systems. I don't know of any seriously proposed voting systems that are non-homogeneous, so this is not a significant extra assumption. Throughout the sequence, I will take for granted that all voting systems are homogeneous.

Assumption 2 is most likely to be violated by voting theorists, as in approval voting and range voting. Next is 3, and there is a small subset of voting theorists who think about non-determinism. Assumption 4 is not very important, and while it is usually made, it also usually does not matter. Assumption 1 is almost never violated, or at least when it is, the field is called something other than voting theory.

A utility function on a set S is just a function from S[0,1]. I will write Δ(S) for the set of distributions on the set S. (I'm not going to worry about the sigma algebras; usually it will be obvious/not matter.)

If f is a voting system, C is a set of candidates, and V∈Δ(C[0,1]) is a distribution on utility functions on C, I will write fC(V) for the output of the voting system on V, so fC(V)∈Δ(C).

Some Important Criteria

To get more comfortable with this formalism, we will translate three important voting criteria.

Condorcet Criterion

If a candidate would defeat all others in one-on-one elections, that candidate should win.

Translated to our formalism, f satisfies the Condorcet criterion if whenever there exists a c∈C such that for all d∈C, we have Pv∼V(v(c)>v(d))>12, we havefC(V)(c)=1.

We can think of Pv∼V(v(c)>v(d)) as saying when we randomly choose a voter v, what is the probability that v prefers c to d. If this probability is greater than 12, then a majority of voters prefer c to d.

Consistency Criterion

If two disjoint el...

Welcome to The Nonlinear Library, where we use Text-to-Speech software to convert the best writing from the Rationalist and EA communities into audio. This is: Popular Personal Financial Advice versus the Professors (James Choi, NBER), published by BrownHairedEevee on October 16, 2022 on The Effective Altruism Forum.

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