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Myopic Calling Strategies

I'm interested in sequential decision-making problems.In these problems, there is a tension between exploration and exploitation. Exploitation is when you take actions with more certainty about the rewards. The goal of exploitation is to get maximum reward to the next action given what is currently known. Exploration is when you take actions with less certainty. The goal is to discover what the rewards are for actions about which little is known.

A strategy that always exploits is called myopic since it always tries to maximize the reward of the current action without any view to long-term gains.

Calling algorithms certainly face this tension. For example, evenings might be the best time on average to contact households. If I know nothing else, then that would be my guess about when to place the next call. But it would be foolish to stay with that option if it continues to fail. If I have failures in that call window, I might explore another call window to try and see if the reward is greater in that window for this particular household.

The following is a simple example, taken from Kulka et al. (1988). The goal is to establish contact. The contact strategy \(a_j\) can take on any of the following five values: WDM=weekday morning, WDA=weekday afternoon, WDE=weekday evening, SAT=Saturday, SUN=Sunday. We want to know which 3-call (\(j=1,2,3\)) sequence produces the highest contact rate. Using our notation, if \(Y_i=1\) denotes contact for the \(i^{th}\) case on any of the 3 calls, then the goal is to find the 3-call sequence that leads to the highest \(Pr(Y_i=1)\). A myopic strategy would choose \(a_1\) by comparing the probability of contact for each of the five possible treatments. The choice of \(a_2\) and \(a_3\) would be made in the same way. A non-myopic strategy would look at all 125 (\(5*5*5\)) possible sequences and determine which one had the highest overall probability of contact. That's basically what Kulka and colleagues did (looking at all possible combinations).

We could extend this approach across several stages of the survey process by looking at how the contact strategy impacts the ability to gain cooperation at later stages. For instance, a three-call sequence that placed three calls in the middle of the night might have a high contact rate, but would likely have a low rate of completing interviews.

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