Psy/Orf 322Feedback on Homework 3 March 2nd 2005
The first experiment called for participants to resolve an inconsistency:
- If a person pulls the trigger then the gun will fire.
- Someone has pulled the trigger.
- But the gun did not fire.
Most participants produced explanations that refuted proposition 1 (the conditional). Your task was to explain this bias. Some of you used the ‘mismatch’ principle in the J-L reading to do so. You received marks for using the reading in this way (provided that you got it right)! Some of you referred to the principle without describing how it works. It predicts that people should give up the conditional, because proposition 3 conflicts with the one mental model of the conditional that has an explicit content:
Pulls-triggerGun-fires.
Proposition 2 says nothing about the gun firing, and so there is no direct conflict between its model and proposition 3. Many of you proposed alternative explanations, e.g.: we are all familiar with guns failing to fire when their triggers are pulled, whereas nothing seems to refute proposition 2. Conditionals are more complex than categorical assertions, and so may be doubted for that reason. You received marks for these ideas. The best answers mentioned both ‘mismatch’ and other ideas, and/or suggested further experimental tests. Some of you wrote that performance in this study was irrational, but it’s hard to see why. Logical reasoning cannot tell you which proposition to give up, but only that have to give up at least one. No-one suggested looking at sentences other than conditionals to test hypotheses!
In problem 2, you had to explain the following rank ordering of probabilities:
(a) A prudent person had unloaded the gun and there were no bullets in the chamber.
(b) A prudent person had unloaded the gun.
(c) There were no bullets in the chamber.
(d) The person didn't really pull the trigger.
As some of you wrote, what is irrational is to rank the probability of a conjunction (a) as greater than the probability of each of its constituent propositions: (b), (c). The ranking violates the probability calculus (see the lecture overheads). The experimental result is an instance of the “conjunction fallacy” discovered by Tversky and Kahneman (see the reading). Some of you argued that (a) is rated as more probable because it is a more “complete” explanation. Some of you drew again on the mismatch principle. The best answers did both. No-one pointed out an artefact in the experiment (at least as described in the homework): explanation (a) is the only assertion in the form of a conjunction. In fact, there was another conjunction in the experiment (a prudent person unloaded the gun and the gun was light), but its second clause doesn’t explain the inconsistency, and it was rated as even less probable than (d). So ‘completeness’ probably means, as many of you suggested, an explanation that refers to both a cause and its effect, where the effect in turn explains the inconsistency. No-one knows for sure what causes these phenomena, and many of your ideas may be correct. The mode of the distribution of marks was 13 out of 20.
Phil J-L.