{"type":"rich","version":"1.0","provider_name":"Transistor","provider_url":"https://transistor.fm","author_name":"80,000 Hours Podcast","title":"#139 – Alan Hájek on puzzles and paradoxes in probability and expected value","html":"","width":"100%","height":180,"duration":13106,"description":"A casino offers you a game. A coin will be tossed. If it comes up heads on the first flip you win $2. If it comes up on the second flip you win $4. If it comes up on the third you win $8, the fourth you win $16, and so on. How much should you be willing to pay to play? \r\n\r\nThe standard way of analysing gambling problems, ‘expected value’ — in which you multiply probabilities by the value of each outcome and then sum them up — says your expected earnings are infinite. You have a 50% chance of winning $2, for '0.5 * $2 = $1' in expected earnings. A 25% chance of winning $4, for '0.25 * $4 = $1' in expected earnings, and on and on. A never-ending series of $1s added together comes to infinity. And that's despite the fact that you know with certainty you can only ever win a finite amount! \r\n\r\nToday's guest — philosopher Alan Hájek of the Australian National University — thinks of much of philosophy as “the demolition of common sense followed by damage control” and is an expert on paradoxes related to probability and decision-making rules like “maximise expected value.” \r\n\r\nLinks to learn more, summary and full transcript.\r\n\r\nThe problem described above, known as the St. Petersburg paradox, has been a staple of the field since the 18th century, with many proposed solutions. In the interview, Alan explains how very natural attempts to resolve the paradox — such as factoring in the low likelihood that the casino can pay out very large sums, or the fact that money becomes less and less valuable the more of it you already have — fail to work as hoped. \r\n\r\nWe might reject the setup as a hypothetical that could never exist in the real world, and therefore of mere intellectual curiosity. But Alan doesn't find that objection persuasive. If expected value fails in extreme cases, that should make us worry that something could be rotten at the heart of the standard procedure we use to make decisions in government, business, and nonprofits. \r\n\r\nThese issues regularly show up in...","thumbnail_url":"https://img.transistorcdn.com/VO1STE7hN95RRg9QdLo4soV2VhhbR9PF5ZZlRhDYcwE/rs:fill:0:0:1/w:400/h:400/q:60/mb:500000/aHR0cHM6Ly9pbWct/dXBsb2FkLXByb2R1/Y3Rpb24udHJhbnNp/c3Rvci5mbS9zaG93/LzQxNDAyLzE2ODM1/NDQ1NDAtYXJ0d29y/ay5qcGc.webp","thumbnail_width":300,"thumbnail_height":300}