Choice Rules and Accumulator Networks

Abstract

This article presents a preference accumulation model that can be used to implement a number of different multi-attribute heuristic choice rules, including the lexicographic rule, the majority of confirming dimensions (tallying) rule and the equal weights rule. The proposed model differs from existing accumulators in terms of attribute representation: Leakage and competition, typically applied only to preference accumulation, are also assumed to be involved in processing attribute values. This allows the model to perform a range of sophisticated attribute-wise comparisons, including comparisons that compute relative rank. The ability of a preference accumulation model composed of leaky competitive networks to mimic symbolic models of heuristic choice suggests that these 2 approaches are not incompatible, and that a unitary cognitive model of preferential choice, based on insights from both these approaches, may be feasible.

Keywords: decision making; heuristics; leaky competitive accumulation; multi-attribute choice; sequential sampling.

Figure 1

The proposed network, which consists of two layers corresponding to attribute representation and preference accumulation, with the attribute representation layer further divided into M sublayers, each corresponding to an attribute. The preference accumulation layer and the attribute representation sublayers each consist of N nodes, with each node corresponding to a possible choice alternative. Additionally, each layer has self-feedback and lateral inhibition, and attribute sublayers are sampled sequentially (with the third sublayer beings sampled here).

Figure 2

Equilibrium activation states for nodes in attribute representation sublayer j, as a function of s_Aj and l_Aj. Here we have x_1j = 0.75, x_2j = 0.5, and x_3j = 0.25.

Figure 3

Parameter values identifying the best alternative on an attribute j (α_1j = 1, α_2j = 0 and α_3j = 0) in the attribute representation sublayer j, as a function of s_Aj and l_Aj. White values indicate parameter values that can make the correct identification. Here we have x_1j = 0.75, x_2j = 0.5, and x_3j = 0.25.

Figure 4

Parameter values identifying the worst alternative on an attribute j (α_1j > 0, α_2j > 0 and α_3j = 0) in the attribute representation sublayer j, as a function of s_Aj and l_Aj. White values indicate parameter values that can make the correct identification. Here we have x_1j = 0.75, x_2j = 0.5, and x_3j = 0.25.

Figure 5

Parameter values that are able to normalize attributes (${\alpha }_{ij}={\omega }_1\cdot x_{ij}-{\omega }_2\cdot {\sum }_{k\ne i}{x}_{kj}$ where ω₁ and ω₂ are positive constants) in the attribute representation sublayer j, as a function of s_Aj and l_Aj. White values indicate parameter values that can perform the correct normalization. Here we have x_1j = 0.75, x_2j = 0.5, and x_3j = 0.25.

Figure 6

Parameter uniqueness as a function of the number of choices the model is applied to. Parameter uniqueness captures the proportion of considered parameter combinations that are the unique best-fit parameters to the data that they generate, in the parameter recovery study.