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Representation Matters: Characterisation and Impossibility Results for Interval Aggregation

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Abstract

In the context of aggregating intervals reflecting the views of several agents into a single interval, we investigate the impact of the form of representation chosen for the intervals involved. Specifically, we ask whether there are natural rules we can define both as rules that aggregate separately the left and right endpoints of intervals and as rules that aggregate separately the left endpoints and the interval widths. We show that on discrete scales it is essentially impossible to do so, while on continuous scales we can characterise the rules meeting these requirements as those that compute a weighted average of the endpoints of the individual intervals.

Dates and versions

hal-03886845 , version 1 (06-12-2022)

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Ulle Endriss, Arianna Novaro, Zoi Terzopoulou. Representation Matters: Characterisation and Impossibility Results for Interval Aggregation. Thirty-First International Joint Conference on Artificial Intelligence (IJCAI-22), Jul 2022, Vienna, Austria. pp.286-292, ⟨10.24963/ijcai.2022/41⟩. ⟨hal-03886845⟩
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