Archive for the 'Innovations' Category

A Modified Algorithm for Evaluating Logical Arguments

A Guest Post

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Bennett Haselton

In a previous guest post I had argued that we should use a random-sample-voting algorithm in any kind of system that promotes certain types of content (songs, tutorials, ideas, etc.) above others. By tabulating the votes of a random sample of the user base, this would reward the content that objectively has the most merit (in the average opinion of the user population), instead of rewarding the content whose creators spent the most time promoting it, or who figured out how to game the system, or who happened to get lucky if an initial “critical mass” of users happened to like the content all at the same time. (The original post describes why these weaknesses exist in other systems, and how the random-sample-voting system takes care of them.)

However, this system works less well in evaluating the merits of a rigorous argument, because an argument can be appealing (gathering a high percentage of up-votes in the random-sample-voting system) and still contain a fatal flaw. So I propose a modified system that would work better for evaluating arguments, by adding a “rebuttal takedown” feature.

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Promise Keeping

So apparently last week, while my attention was directed elsewhere, Donald Trump attempted to attract the support of conservatives by promising to choose all of his Supreme Court appointments from a short list of candidates who he believes conservatives will find appealing.

Regardless of what you think of those individual candidates, there is absolutely no reason this gambit should garner support from conservatives for the simple reasont that the promise is not enforceable. This would be a problem with any politician, but particularly with Trump, who has never felt any qualms (or even, as far as I can see, any embarrassment) about shifting his positions 180 degrees from one day to the next.

But there’s a way to fix that problem, and it’s available not just to Trump but to any politician with credibility issues. Let him issue a list of specific promises (such as “All of my Supreme Court appointments will come from this list”) and then put the bulk of his personal wealth in an escrow account, to be returned to him if he loses the election or if he serves and keeps his promises — and to be paid to someone else if he’s elected and breaks those promises. The named beneficiary could be, for example, the U.S. Treasury, or — if the candidate is particularly concerned about attracting the votes of traditional Republicans — the Republican National Committee.

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An Algorithm For An Automated Meritocracy

A Guest Post

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Bennett Haselton

A 2006 study by Matthew Salganik and his co-researchers at Princeton suggests that a huge amount of effort is wasted in many different areas of human endeavor, and the resulting outcomes are far less than optimal — but that there is a simple algorithm that could fix both problems.

In Salganik’s experiment, users of a music-rating site were divided at random into eight artificial “worlds”. All of the users in all eight worlds had access to the same library of songs, which they could download or recommend to their peers, but they could only recommend songs to other users in the same world. Also, each user could view the number of times that a song had been downloaded, but only by other users in the same world.

The goal was to see whether certain songs could become popular in some worlds while languishing in others, despite the fact that all groups consisted of randomly assigned populations that all had equal access to the same songs. The experiment also attempted to measure the “merit” of individual songs by assigning some users to an “independent” group, where they could listen to songs and choose whether to download them, but without seeing the number of times the song had been downloaded by anyone else; the merit of the song was defined as the number of times that users in the independent group decided to download the song after listening to it. Experimenters looked at whether the merit of the song had any effect on the popularity levels it achieved in the eight other “worlds”.

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Political Strategy

It now seems likely that:

  • In order for either Ted Cruz or Marco Rubio to become the Republican nominee, he must first consolidate the anti-Trump vote, which is to say that either can succeed only if the other drops out.
  • Cruz and Rubio have approximately equal chances of driving each other out.
  • Each would prefer to drive the other out sooner rather than later — i.e. before Trump wraps this whole thing up anyway.

Given that, it seems like one of the following two things should happen at tonight’s debate:

    Either:

  1. Cruz, after making an eloquent case against Trump and explaining why he thinks it’s important to keep Trump out of the White House, turns to Rubio and offers to flip a coin right on the spot. The loser drops out of the race and the winner takes on Trump.
  2. or

  3. Rubio, after making an elegant case against Trump and explaining why he thinks it’s important to keep Trump out of the White House, turns to Cruz and offers to flip a coin right on the spot. The loser drops out of the race and the winner takes on Trump.

This gives each of them only a 50% chance of survival. But if they’ve already each got only a 50% chance of survival, that’s no loss. And it substantially increases the value of survival, because it gets things over with now instead of a month from now.

If I’m wrong in saying that each currently has a 50% chance — if instead, say, Cruz has a 60% chance and Rubio a 40% chance or vice versa — then they can flip an appropriately weighted coin.

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A Curious Oversight

Got a great idea but don’t want to start a business? The Wall Street Journal offers a menu of strategies — but omits my favorite: Buy a whole lot of stock in a company that you believe could profit from your idea, and then give them the idea for free. It’s imperfect, but so’s everything else, including starting a business.

Most great enterprises require plenty of innovation, hard work and risktaking. One of the reasons capitalism works so well is that it enables the innovators, the hard workers and the risk takers to be different people, by providing institutions that allow them to coordinate their efforts. The stock market is one of those institutions. This isn’t something I’d have expected the Wall Street Journal to overlook.

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Blind Spots

beatlesThe other night at dinner, I was asked whether, when the Beatles came to the US in 1963, I had had any sense that something really big had happened.

Well, I was pretty young in 1963, probably too young to think about such matters. I remember having little interest in the Beatles, but being being very aware that they were something very big. Everyone was aware of that. But unless I am mistaken, pretty much nobody realized that we were witnessing something really big and lasting. More generally, I doubt that anyone at the time had any inkling of the long-term significance of rock ‘n’ roll. We knew it was popular, but we had no idea it would change the world. I’m not sure that in 1963 anyone knew that it was possible for music to change the world.

This led to the more general question: How quickly are great cultural watersheds recognized for what they are? In the few areas I know something about, I think the answer is “usually pretty quickly”. I remember 1910 even less vividly than I remember 1963, but I am pretty sure that it wasn’t long between the appearance of The Love Song of J. Alfred Prufrock and the realization (at least among people who care about this sort of thing) that poetry had changed forever. In mathematics, at least in the past century (and I’m pretty sure for several centuries, or even millenia, before that), major paradigm shifts have generally been recognized very quickly. When a Serre or a Grothendieck upends the mathematical world, the mathematical world quickly knows it’s been upended.

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Make Them Gamble

A Guest Post

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Jamie Whyte

Last week, Britain had a referendum to decide whether or not to replace its current “first past the post” electoral system with the alternative vote system (AV). During the campaign, the No to AV campaign claimed that changing to AV could cost £250 million, in part because voting machines would be introduced with it. Yes campaigner and member of parliament, Simon Hughes claimed that this was false and that the No campaigners knew it was. He asked the electoral commission to stop the No campaigners from lying.

Similar appeals are often made by other frustrated political disputants. But the idea that electioneering politicians should be allowed to say, and voters to hear, only what the electoral commission deems to be true and honestly believed is outrageous. It would make election outcomes depend on the judgement, not of the voters, but of the electoral commissioners.

The proposal is also unnecessary. As anyone who has argued with blowhards will know, there is an easy way of showing that someone does not really believe what he says. Challenge him to a wager. Demand that he put his money where his mouth is.

If the No campaigners really believe that changing to AV would cost £250 million, they will be willing to bet on it. By offering the wager, and having it declined, Mr Hughes would expose their insincerity. Equally, Mr Hughes’ failure to suggest the wager may tell us something about his own alleged certainty on the matter.

Politicians should generally be obliged to bet on the outcomes their various claims. This would discourage their lying which, incredible as it may sound, is even more widespread than people working with the standard definition of lying realise.

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Blogging, Tic Tac Toe and the Future of Math

Blogging, as you might have heard, is changing the face of the media. It may also be changing the face of mathematical research. For the first time ever, a substantial mathematical problem has been solved via an accumulation of blog comments, all building on each other. Could this be the future of mathematical research?

Before I explain the problem, let’s talk a little about tic-tac-toe. As you probably figured out long ago, intelligent players of ordinary tic-tac-toe (on a 3 by 3 board) will invariably battle to a draw. But, as you probably also figured out, not every game ends in a draw, because not every player is intelligent.

On the other hand, if we blacken out the three squares on the main diagonal and don’t allow anyone to play there (so the game ends when the remaining six squares are filled, then every game is sure to end in a draw. There’s simply no way to get three in a row when you’re not allowed to play on the diagonal:

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Fewer Voters Are Better Voters

A Guest Post

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Jamie Whyte

Last year, the British government decided to lift the top rate of income tax from 41 to 52 percent. Last month, Lord Myners, the UK Secretary of State for Financial Services, said that the policy would raise not nearly as much revenue as had been expected. People are apparently making efforts to avoid paying it. A host of politicians and commentators responded that it was always a foolish idea, a purely “political” policy.

But how can a bad policy be good politics? What defect in the electoral system can explain this?

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