A MODEL OF OPTIMAL EXPLORATION AND DECISION MAKING IN NOVEL INTERFACES

Keywords:

Introduction

Below we propose a model of first command choice that is intended to explain some of these effects. Our style of explanation is to conduct a "rational analysis", following Anderson [3]. That is, we try to understand subject behavior as optimal adaptations to the task.

ASSUMPTIONS OF THE MODEL

Our second assumption is that users encode an estimate of the relevance of a command given its label, where by "relevance" we mean how likely it is that the command is the one required to carry out the current task. The estimated relevance of the ith command is referred to as Ri. The set of relevances for all commands in the interface is referred to as R. Our third assumption is that users come with prior experiences concerning the usefulness of a command's relevance estimate as a predictor for determining whether the command is the correct one for accomplishing the task. From all the times in the past when a correct command was selected, the user may form what we will call a "signal" probability distribution (denoted P(Ri|S)) which indicates how relevant correct commands are likely to appear. From all the times in the past when an incorrect command was selected, the user may form what we will call a "noise" probability distribution (denoted P(Ri|N)) which indicates how relevant incorrect commands are likely to appear. Our use of the terms "signal" and "noise" are borrowed from signal detection theory, as we have been viewing the correct command as the signal that must be detected against a background of noise (incorrect commands).

Figure 1. Example signal and noise distributions.

Figure 1 presents an example of signal and noise distributions, in which relevance is treated as a discrete variable ranging from 1 to 7. The signal distribution indicates that correct commands most often come with a relevance of 5, but sometimes as high as 7 and as low as 3. The noise distribution indicates that incorrect commands most often come with a relevance of 3, but sometimes as high as 5 and as low as 1. The overlapping signal and noise distributions is a way of indicating that the label is not a foolproof indicator of the usefulness of a command. Once again we appeal to the analogy with signal detection theory: If one adopts a low threshold then incorrect commands will often be chosen, but if one adopts a high threshold then correct commands will often be overlooked. Our final assumption is that the user knows the number of commands in the interface, which we refer to as K.

THE MODEL

Employing the Anderson decision making framework [3], the next action that one chooses should be the one with the greatest expected value. In our case, this will reduce to choosing the action (scanning or executing) with the least expected cost of finding the correct command.

Calculating costs.

    
Cscan	=	KCmove/2 +  		(1)    
			[1-P(Hbest(1)|R)]*(Cundo+KCmove/2 +    
				[1-P(Hbest(2)|R)]*(Cundo+KCmove/2 +    
					etc.))   

However, the model predicts that a command will always be chosen no later than on the second pass, which is clearly at odds with phenomenon (3). One possibility is that users do not remember the relevance of all the labels that were scanned over during the first pass, so that there is a still a great deal of uncertainty over what might appear in the interface. The model could be enhanced to include a parameter that determined the probability of encoding the relevance of a command. The model also does not predict phenomenon (4), the fact that people seem to slow down as they make successive passes over the interface. We speculate that users are spending more time considering a command in order to semantically elaborate the command label more deeply, and to perform more extensive envisionments of what effect the command might have.

Acknowledgments

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