Tag Archives: Flipping Coins

Choice Architecture: Even in “Heads or Tails,” It Matters What’s Presented First

If you’re familiar with behavioural economics, then the results of this study will be right up your alley.

The researchers set out to determine whether there was a “first-toss Heads bias.” Meaning, when flipping a coin and the choices are presented “Heads or Tails,” there would be a bias towards people guessing “Heads” (because it was presented first). Through running their tests, they found something else that surprised them [Emphasis Added]:

Because of stable linguistic conventions, we expected Heads to be a more popular first toss than Tails regardless of superficial task particulars, which are transient and probably not even long retained. We were wrong: Those very particulars carried the day. Once the response format or verbal instructions put Tails before Heads, a first-toss Tails bias ensued.

Even in something as simple as flipping a coin, something where the script “Heads or Tails” is firmly engrained in our heads, researchers discovered that by simply switching the order of the choices, the frequency with which people chose one option or the other changed. That’s rather incredible and possibly has implications from policy to polling. However:

There is, of course, no reason to expect that, in normal binary choices, biases would be as large as those we found. In choosing whether to start a sequence of coin tosses with Heads or Tails, people ostensibly attach no importance to the choice and therefore supposedly do not monitor or control it. Since System 1 mental processes (that are intuitive and automatic) bring Heads to mind before Tails, and since there is no reason for System 2 processes (which are deliberative and thoughtful; see, e.g., Kahneman & Frederick, 2002) to interfere with whatever first comes to mind, many respondents start their mental sequence with Heads. However, in real-life questions people often have preferences, even strong ones, for one answer over another; the stronger the preference, the weaker the bias. A direct generalization from Miller and Krosnick (1998) suggests that in choices such as making a first-toss prediction, where there would seem to be no good intrinsic reason to guide the choice, order biases are likely to be more marked than in voting. At the magnitude of bias we found, marked indeed it was. Miller and Krosnick noted with respect to their much smaller bias that “the magnitude of name-order effects observed here suggests that they have probably done little to undermine the democratic process in contemporary America” (pp. 291–292). However, in some contexts, even small biases can sometimes matter, and in less important contexts, sheer bias magnitude may endow it with importance.

OK, so maybe these results don’t add too much to “government nudges,” but it can — at a minimum — give you a slight advantage (over the long haul) when deciding things by flipping coins with your friends. How?

Well, assuming that you are the one doing the flipping, you can say to your friend: “Tails or Heads?” (or “Heads or Tails?”) and then be sure to start the coin with the opposite side of what your friend said, facing up. A few years ago, Stanford math professor Persi Diaconis showed that the side facing up before being flipped is slightly more likely to be the side that lands facing up.

ResearchBlogging.orgBar-Hillel M, Peer E, & Acquisti A (2014). “Heads or tails?”–a reachability bias in binary choice. Journal of experimental psychology. Learning, memory, and cognition, 40 (6), 1656-63 PMID: 24773285

Don’t Fall for the Gambler’s Fallacy: List of Biases in Judgment and Decision-Making, Part 7

A little later in the day than I would have liked, but today’s cognitive bias is the gambler’s fallacy. The bias gets its name from, as you’d expect, gambling. The easiest example to think of is when you’re flipping a coin. If you flip a coin 4 times and each of those 4 times the coin turned up heads, you’d expect the coin to turn up tails on the next (or at least have a higher chance of turning over tails), right? WRONG!

The odds are exactly the same on the 5th turn as the 6th turn as the 66th turn as the 11,024th turn. Why? Because the two instances of flipping the coin are independent events. (Note: we’re ignoring, for the time being, any effects that quantum reality might have on a given event in the past and the future.) So, every time you flip a coin, that’s an independent event — unaffected by earlier events.

Another important example is the reverse fallacy. That is, if we think that heads are “hot” because it’s been flipped a number of time, thinking that there’s a better chance that heads will be flipped is also a fallacy. Again, this is an independent event — unaffected by previous events.

This fallacy is so named because there’s a famous example of the gambler’s fallacy happening at the Monte Carlo Casino where, on roulette, black came up 26 times in a row. A number of gamblers reasoned that red would come up because there had been such an unlikely number of blacks that came up in a row. As the story goes, they lost millions.

Other examples of the gambler’s fallacy:

  • Childbirth: “we’ve had 3 boys, so we’re going to have a girl now…”
  • Lottery: “I’ve lost 3,000 times, so I’m due for a win…”
  • Sports: “Player X is playing really well, they’re bound to start playing bad…”
  • Stock market: “Stock X has had 7 straight down days, so it’s bound to go up on this next trading day…”

Ways for Avoiding the Gambler’s Fallacy

1) Independent Events vs. Dependent Events

The biggest way to avoid the gambler’s fallacy is to understand the difference between an independent event and a dependent event. In the classic example, the odds of a coin landing on heads or tails is — negligibly — 50/50 (I say negligibly because there are those who contend that the “heads side” weighs more and thus gives it a slight advantage). An example of a dependent event would be picking cards from a deck. There are 52 cards in a deck and if you pick one card without replacing it, your odds of picking one of the other 51 cards increases (ever so slightly).

If you liked this post, you might like one of the other posts in this series: