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Vagueness and aggregation in multiple sender channels

Research output: Contribution to journalArticle

Original languageEnglish
Number of pages38
JournalErkenntnis
Early online date22 Mar 2017
DOIs
StateE-pub ahead of print - 22 Mar 2017

Abstract

Vagueness is an extremely common feature of natural language, but does it actually play a positive, efficiency enhancing, role in communication? Adopting a probabilistic interpretation of vague terms, we propose that vagueness might act as a source of randomness when deciding what to assert. In this context we investigate the efcacy of multiple sender channels in which senders choose assertions stochastically according to vague definitions of the relevant words, and a receiver then aggregates the different signals. These vague channels are then compared with Boolean channels in which assertions are selected deterministically based on classical (crisp) definitions. We show that given a sufficient number of senders, a linear stochastic channel outperforms Boolean channels when performance is measured by the expected squared error between the actual value described by the senders and the receiver's estimate of it based on the signals they receive. The number of senders required for vague channels to be at least as accurate as Boolean channels is shown to be a decreasing function of the size of the language i.e. the number of description labels available to the senders. Vague channels are then shown to be robust to transmission error provided the error rate is not too large. In addition, we investigate the behaviour of both Boolean and vague channels for a parametrised family of distributions on the input values. Finally, we consider optimal vague channels assuming a fixed number of senders and show that, provided there are more than two senders, a vague channel can be found that outperforms the optimal Boolean channel.

    Research areas

  • Vagueness, communication, Stochastic Assertions, Multiple Senders Channels

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    Rights statement: This is the final published version of the article (version of record). It first appeared online via Springer at http://link.springer.com/article/10.1007%2Fs10670-016-9862-2. Please refer to any applicable terms of use of the publisher.

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