Tag: Probability

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(This post won’t make much sense unless you’ve read Part 1. Sense not guaranteed even if you have.) The Keys to a Shiny New Australia Let’s say I’m in a no-holds-barred game of RISK with @SaintAugustine.* He’s fortified Australia, but I’ve got cards. I plop the cards down; after a grueling campaign it’s come down […]

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Fun with Markov Chains


Wait, what’s a Markov Chain, and why do I care? A Markov chain is a tool for understanding probabilities. Specifically, it’s useful for calculating sequences of probabilities. We’re going to look at three cases:

  • Easy: Russian Roulette
  • Slightly harder: Fetching a beer
  • Complicated: Conquering Australia

Ready to begin? Let’s go!

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This is, I suppose, about as off-the-wall as a question can be, but my memory has once again failed me.  Many many years ago I read a story, surely science fiction, wherein the author posited that the number of pleasing musical score had to be a finite number.  As I recall, there was something in […]

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Maybe, Baby


If you knew you only had a 1% chance of surviving tomorrow, would you consider that a death sentence? What about 2%, 5%, 10%… at what point would your odds of survival be good enough you wouldn’t feel doomed? And what if you had to purchase your fairly slim chance at survival by risking the life of another? When would you do it? What balance of risk would just barely escape counting as doom?

What if you were the other whose life was risked on the slim hope of avoiding someone else’s death sentence? When would that hope be worth it, and when would it be a forlorn one? How effective must our efforts to lift another’s doom be in order to merit the price?

Musings of a Third-Generation Wagon Circler


Writing here at Ricochet last week, @KateBraestrup expressed her opinion that “even without the sixfold imprimatur of the FBI, it would be virtually impossible to make a circle of wagons tight enough to conceal the kind of lurid behavior that Kavanaugh has been accused of.” She continued: “It’s not that it doesn’t exist; rather, when it exists, people know about it. Louche, lascivious or predatory men (alcoholic or otherwise) over time become well-known for being so.” While I’m relieved Kavanaugh has been confirmed, and I dreaded the precedent that would have been set if he had not have been, I can’t agree that men’s wagon circles are virtually never this tight. I know because I’m part of more than one man’s wagon circle, as was my mother, and her mother before her. Three generations of conservative American women, all three with little inclination to laugh off predatory behavior as just “boys being boys” — and all three with just as little inclination to name and shame men for having stories like those alleged about Kavanaugh in their past.

Men become notorious for sexual predation by persisting in it for long periods of time, especially if they become shameless about it. One reason we caution youth to postpone sex is because immature sexual misadventures are often exploitative. As Mark Regnerus has documented in his books Premarital Sex in America: How Young Americans Meet, Mate, and Think about Marrying and Forbidden Fruit: Sex & Religion in the Lives of American Teenagers, boys usually find it considerably easier than girls do to self-servingly and callously rationalize their “conquests,” even when they’ve had the moral formation to know better. Thank God that boys who should know better and don’t often mature into men who know better and do! Thank God that not everyone who has committed a sexual wrong in his past persists in that sort of misbehavior.

Thoughts on Tiamat this Electoral Eve


The maples, wicks of autumn, go to cinder from the top down, the blaze on most trees past its prime, now mostly scattered at our feet. The plant kingdom burns brightly as it plunges into wintry darkness. A plunge into some outcome or another awaits us tomorrow, too. We can estimate what it might be – and we should. But as Ricochet Member @rodin reminds us, “none of us will ever know (or at least [not] for a long long time) whether the way we cast our ballot was better than the alternative.”

All this fall, I’ve had an unknown greater than the outcome of this election hanging over my head – or at least greater to me. One reason it’s greater is that I’m more responsible for it. However I vote, whatever I say, the outcome of this election is largely out of my hands. This other thing, though, is very much in my hands, or it’s supposed to be, and so the moral weight I bear for its unknown nature is far greater than the weight I bear for my vote.

Odds and the Moral Obligation


Merely disagreeing with the way another person plans to vote isn’t tantamount to questioning that other person’s morality. Insisting that “It’s morally imperative to vote my way” or “Those voting differently from me are _____” where _____ is some sort of moral flaw (preening, cowardice, squeamishness, etc) isn’t just disagreeing with how others plan to vote, though.

I look at the question, “Do the odds in my state of my vote flipping the election to the victor give me a moral obligation to choose between the two leads?” as a prudential question that depends on a judgment call about those odds. Knowing the lottery-like nature of those odds, typically even in swing states, I can understand anyone answering, “No.” I can also understand those in swing states answering yes. Or anyone answering yes for himself, if entering the lottery for the victor, even with the smallest odds imaginable, is important to him. Where to set bounds like “so close to zero it may as well be” is always a judgment call in decision making, not something that can be established by mathematical proof.

Other Candidates Got Your Down? Hoist Yer Stein!


American Stein HoistPolitics is a dirty game and nobody has to like federal funding of elections to be resigned to the observation that it’s unlikely to go away anytime soon. Given this observation, what might we do with it? The virtue of strategic, rather than principled, voting – or rather, the assertion that strategic voting is, in reality, the only form of principled voting – has many champions among the Ricochetti this year. Nonetheless, even if we grant that the odds of one’s vote being decisive are large enough in swing states that swing-state voters should feel morally obligated to choose between the two lead candidates (those odds are around one in ten million), many of us live in states so far from swing that they’re not even on the playground (our odds are more like one in a billion).

As of this morning, my state has around a 0.2% chance of tipping the election, and is one of 20 states whose voter power index is under 0.1 (a vote in New Hampshire is more than 50 times more likely than mine to decide the election), according to FiveThirtyEight. (If you don’t like Nate Silver’s methodology, feel free to substitute whichever prediction system you trust most.) Meanwhile, Gary Johnson is polling at around 8 percent nationally. Now, it’s common for polling to overestimate the share of votes third-party candidates will get. Nonetheless, if Johnson is polling at 8 percent now, he has a serious chance of crossing the threshold necessary for the Libertarian Party to receive FEC funding, which is 5 percent of the popular vote. Moreover, as @matt.corbett put it in his recent OP,

As a matter of good public choice theory, sitting out or voting third party (or advocating either) is entirely defensible as part of a long-term strategy. The great paradox of voting coalitions is that the least reliable members have the most influence… Influence can only be re-established with credibility, and credibility can only be re-established by action. An election where “your” candidate is openly contemptuous of you and is most likely a loser anyway is the ideal time to protest vote.

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What is luck? Is it just a form of probability that we notice? I remember reading somewhere that if one were to have thirty random people in the room, the probability is that two would share the same birthday. One would think that the probability would not approach unity until one had as many people […]

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