21.5.1 Modelling an Individual’s Satisfaction on its Own
In [12], we investigated four satisfaction functions to model an individual’s satisfaction. We compared the predictions of these satisfaction functions with the predictions of real users. We also performed an experiment (see Figure 21.4) to compare the predictions with the real feelings of users.
The satisfaction function that performed best defines the satisfaction of a user with a new item i after having seen a sequence items of items as:
Parameter ? represents satisfaction decaying over time (with ? =0 past items have no influence, with ? =1 there is no decay).
Parameter ? represents the influence of the user’s satisfaction after experiencing previous items on the impact of a new item. This parameter is inspired by the psychology and economics literature, which shows that mood impacts evaluative judgement [12]. For instance, half the participants answering a questionnaire about their TVs received a small present first to put them in a good mood. These participants were found to have televisions that performed better. So, if a user is in a good mood due to liking previous items, the impact of an item they normally dislike may be smaller (with how much smaller depending on ? ).
Parameters ? and ? are user dependent (as confirmed in the experiment in [12]). We will not define Impact(i) in this chapter, see [12] for details, but it involves quadratic ratings and normalization as found in the experiment discussed above.