Choice deferral, indecisiveness and preference for flexibility

In a standard model of menu choice, we examine the behavior of an agent who applies the following Cautious Deferral rule: “Whenever in doubt, don't commit; just leave options open.” Our primitive is a complete preference relation ≽ that represents the agent's choice behavior. The agent's indecisiveness is captured by means of a possibly incomplete (but otherwise rational) preference relation ≽ˆ. We ask when ≽ can be viewed as a Cautious Deferral completion of some incomplete ≽ˆ. Under the independence and continuity assumptions commonly used in the menu choice literature, we find that even the smallest amount of indecisiveness is enough to force ≽, through the above deferral rule, to exhibit preference for flexibility on its entire domain. Thus we highlight a fundamental tension between non-monotonic preferences, such as preferences for self-control, and tendency to defer choice due to indecisiveness.