How many people will select the same option as you?

The slashdots site had a recent "survey" that prompted a lot of discussion. I won't try to collect your response here, that would count as one of those reading "interruptions" that I try to avoid, but it had just one simple question in it:

How many people will select the same option as you?

• 0%
• 1-25%
  
• 26-50%
• 51-75%
• 76-99%
• 100%

It looks very obvious. Cognitive Daily summed up the basic proposition:

At first pass, you might figure that there are 6 possible responses, so if people respond randomly then about 16 percent will choose each answer, so the correct response would be 1-25 percent. But of course, if everyone used that same logic, then many more than 25 percent of respondents would choose that answer. The next logical response would be to move on to 26-50 percent. But once again, if everyone used that logic, the correct response would be higher still.

Very sensible analysis. If over-analysed then it might seem paradoxical. But basically common sense. I do have one further point, for as with my dislike of interruptive multimedia, another blog rule is that I do not just post stuff without adding an original thought. Incidentally, I guessed correctly. Even more incidentally, I work in marketing.

In marketing, we cannot stock every alternative, so we regularly have to predict the "most popular option". Of course that is not necessarily the option that we personally would choose, despite overblown arguments for "you must have personal experience of what you are selling".

For we try to predict the option that the consumer will choose, but that is not necessarily the option that the consumer should choose. We also need to account for the influence of other people's selections upon that choice. We need to guess the proportion of people who will behave rationally, the proportions who will act in isolation or in collusion. We should determine the evolving Nash equilibria. We should resolve the prisoner's dilemma.