The Consensual Dynamics of Random Debates with Explicit Background Knowledge
The simulations presented in the last chapter suggest that the overall prospects of reaching agreement due to argumentation are bleak as long as arguments are introduced randomly and as long as there are no commonly agreed upon background beliefs. In the
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The Consensual Dynamics of Random Debates with Explicit Background Knowledge
The simulations presented in the last chapter suggest that the overall prospects of reaching agreement due to argumentation are bleak as long as arguments are introduced randomly and as long as there are no commonly agreed upon background beliefs. In the following, we take background knowledge into account by explicitly fixing the truth values assigned to some of the sentences, and investigate whether this fosters the rapprochement of proponent positions.
5.1 Setup Argumentation Mechanism: Arguments are introduced in accordance with random argumentation (cf. Sect. 4.1), which is supplemented by the additional verification that the new argument does not render the background knowledge incoherent. Discovery Mechanism: The background knowledge Bt fixes the truth values of a specific proportion β (namely, 10%, 20%, and 40%) of the n sentence pairs in the sentence pool. It remains constant throughout the debate simulation. Update Mechanism: Positions are updated according to a modified closest coherent mechanism (cf. Sect. 4.1), taking background knowledge into account. More specifically, once τt+1 is determined, it is checked (for every i = 1 . . . 6) whether Pti is coherent on τt+1 and extends Bt+1 . If it does, the position i remains i = P i ). If it doesn’t, P i unchanged (Pt+1 t t+1 is set to the closest coherent position i i to Pt which extends Bt+1 ; that is, Pt+1 is that position P ∈ Γτt+1 (Bt+1 ) with minimal Δ (P, Pti ). In case there are several closest τt+1 -coherent positions, one of those is chosen randomly. Let us call this mechanism closest coherent with background knowledge.
G. Betz, Debate Dynamics: How Controversy Improves Our Beliefs, Synthese Library 357, DOI 10.1007/978-94-007-4599-5 5, © Springer Science+Business Media Dordrecht 2013
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5 Background Knowledge
Initial proponent positions are assigned so as to be consistent with (i.e., so as to extend) the background knowledge. A debate contains six proponent positions. Three ensembles with β = 0.1, β = 0.2, and β = 0.4 are generated, each containing 1,000 individual debate simulations.
5.2 Results Figure 5.1 plots the mean agreement evolutions corresponding to the three ensembles. Given that all positions agree at least with regard to the sentences which belong to the background knowledge, two randomly assigned positions differ, on average, with respect to half of the sentences which are not included in the background knowledge. This is the reason why ensemble-wide mean agreement evolutions take off at an initial value equalling 0.5 + β /2. As the left-hand plots illustrate, a controversial argumentation becomes significantly more effective in terms of generating agreement once a shared background knowledge is established. At a density of 0.5, mean agreement has increased, relative to its initial value, by roughly 15 percentage points for β = 0.1. If the background knowledge comprises 20% or 40% of the sentences, argumentation raises the initial agreement even
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