We Should Communicate Probabilities With Flips
tags: #probability
Flipping Coins
If someone walks up to you and offers $100,000 if they flip a coin and it lands heads, you’re correct in believing that you have no means of predicting the outcome. If that same person offers you the same bet on a weighted coin with a 60% chance of heads, all of a sudden you’re daydreaming about what cool new car you’re going to buy. If the coin has a 90% chance of heads, you’re mentally putting the deposit down on the new car long before the coin enters the air. This is bad thinking, this is a base 10 problem, and this can be solved.
Flipping Multiple Coins
Our someone changes the bet: you win unless she flips 3 tails in a row. This feels… different. Is that deposit refundable? The first thing we learn about probability is the multiplication rule: your odds of losing in this new game are 12.5%, giving you pretty close to the 90% chance of buying your new Audi. But suddenly, this feels bad. You can envision losing.
The problem with communicating probabilities with decimals is that 60% feels monumentally bigger than 50%, and 90% feels so close to 100% that it’s not even worth thinking about. Multiplying these numbers by 10 doesn’t help -- even if 9 in 10 dentists recommend a toothbrush (an entire dentist doesn’t like the toothbrush!), it’s still a sure thing since 9 feels really close to 10.
The “Flip” as a Unit
We can solve our base 10 problem with a new unit: the flip. Two conversion tables are below, and are relative to the concept of the “winning outcome” or the “losing outcome”. The colors in the tables reflect reckless optimism on the top and loss aversion on the bottom. Choose the top if you’re watching basketball, and a more extreme version of the bottom if you’re running a nuclear power plant.
What we notice here is that with flips, 60% hardly feels better than 50% in our one shot betting situation. That doesn’t mean 60% isn’t better than 50%, but we need to be careful using these probabilities to change our planning and decision making. When the weather forecaster says there’s a 70% chance of rain or Nate Silver says [insert candidate here] has a 71.4% chance of winning a presidential election, they are still delivering information, but not quite as much as our base 10 communication system would lead you to believe.