Limits...
The 2N-ary Choice Tree Model for N-Alternative Preferential Choice.

Wollschläger LM, Diederich A - Front Psychol (2012)

Bottom Line: It implements pairwise comparison of alternatives on weighted attributes into an information sampling process which, in turn, results in a preference process.Then it is shown how the model accounts for several context-effects observed in human preferential choice like similarity, attraction, and compromise effects and how long it takes, on average, for the decision.A short discussion on how the 2N-ary choice tree model differs from the multi-alternative decision field theory and the leaky competing accumulator model is provided.

View Article: PubMed Central - PubMed

Affiliation: School of Humanities and Social Sciences, Jacobs University Bremen Bremen, Germany.

ABSTRACT
The 2N-ary choice tree model accounts for response times and choice probabilities in multi-alternative preferential choice. It implements pairwise comparison of alternatives on weighted attributes into an information sampling process which, in turn, results in a preference process. The model provides expected choice probabilities and response time distributions in closed form for optional and fixed stopping times. The theoretical background of the 2N-ary choice tree model is explained in detail with focus on the transition probabilities that take into account constituents of human preferences such as expectations, emotions, or socially influenced attention. Then it is shown how the model accounts for several context-effects observed in human preferential choice like similarity, attraction, and compromise effects and how long it takes, on average, for the decision. The model is extended to deal with more than three choice alternatives. A short discussion on how the 2N-ary choice tree model differs from the multi-alternative decision field theory and the leaky competing accumulator model is provided.

No MeSH data available.


Transition probabilities for the two-alternative choice problem with no counter-dependent and random component. p(A+), p(B)+, p(A)+, and p(B−) sum up to one and are the same for the outgoing edges of each vertex v ∈ V.
© Copyright Policy - open-access
Related In: Results  -  Collection

License
getmorefigures.php?uid=PMC3378970&req=5

Figure 3: Transition probabilities for the two-alternative choice problem with no counter-dependent and random component. p(A+), p(B)+, p(A)+, and p(B−) sum up to one and are the same for the outgoing edges of each vertex v ∈ V.

Mentions: Three features of the model are of specific interest: (a) when and how the walk starts after presentation of choice alternatives (in an experimental trial), (b) how the walk chooses the next edge to pass through in each step, and (c) when and how the walk stops. Without an a priori bias toward any of the choice alternatives, we assume that all counter states are set to zero at the outset of the information sampling process and hence, the process starts with presentation of the choice alternatives. Biases toward one or several of the alternatives can be implemented by either defining initial values unequal to zero for these alternatives or by independently sampling information for the alternatives from predefined distributions for some time before the actual information sampling process starts (cf. Diederich and Busemeyer, 2006; Diederich, 2008). For simplicity, we assume no biases here, i.e., initial values are set to zero for all alternatives. Note that for the 2N-ary choice tree, initial values are counter states at the root r. Then the walk moves away from there step by step, choosing the next edge to pass through by means of so-called transition probabilities pe, e ∈ E. The transition probabilities are built up of the comparison of the alternatives the decision maker considers and supplemented with a counter-dependent component and a random component. For each vertex, the transition probabilities for all outgoing edges sum up to one, so that the walk does not stay still at any vertex it reaches throughout the information sampling process. We show the structure of the model first; a detailed description of the transition probabilities is presented in the next section. For simplicity consider a choice situation with two alternatives A and B; the counter-dependent component and the random component are set to zero. As shown in Figure 3, transition probabilities are the same for the outgoing edges of each vertex v ∈ V, i.e., for each edge (v,v(A+)) ∈ E leading to a vertex with label A+, for each edge leading to a vertex with label B+ and so on for the other counters A− and B−. The probability for walking along a specific path is the product of transition probabilities of all edges on that path. In our example, the probability p for making the first three steps as shown in Figure 2 is p = p(B+)·p(A−)·p(B+).


The 2N-ary Choice Tree Model for N-Alternative Preferential Choice.

Wollschläger LM, Diederich A - Front Psychol (2012)

Transition probabilities for the two-alternative choice problem with no counter-dependent and random component. p(A+), p(B)+, p(A)+, and p(B−) sum up to one and are the same for the outgoing edges of each vertex v ∈ V.
© Copyright Policy - open-access
Related In: Results  -  Collection

License
Show All Figures
getmorefigures.php?uid=PMC3378970&req=5

Figure 3: Transition probabilities for the two-alternative choice problem with no counter-dependent and random component. p(A+), p(B)+, p(A)+, and p(B−) sum up to one and are the same for the outgoing edges of each vertex v ∈ V.
Mentions: Three features of the model are of specific interest: (a) when and how the walk starts after presentation of choice alternatives (in an experimental trial), (b) how the walk chooses the next edge to pass through in each step, and (c) when and how the walk stops. Without an a priori bias toward any of the choice alternatives, we assume that all counter states are set to zero at the outset of the information sampling process and hence, the process starts with presentation of the choice alternatives. Biases toward one or several of the alternatives can be implemented by either defining initial values unequal to zero for these alternatives or by independently sampling information for the alternatives from predefined distributions for some time before the actual information sampling process starts (cf. Diederich and Busemeyer, 2006; Diederich, 2008). For simplicity, we assume no biases here, i.e., initial values are set to zero for all alternatives. Note that for the 2N-ary choice tree, initial values are counter states at the root r. Then the walk moves away from there step by step, choosing the next edge to pass through by means of so-called transition probabilities pe, e ∈ E. The transition probabilities are built up of the comparison of the alternatives the decision maker considers and supplemented with a counter-dependent component and a random component. For each vertex, the transition probabilities for all outgoing edges sum up to one, so that the walk does not stay still at any vertex it reaches throughout the information sampling process. We show the structure of the model first; a detailed description of the transition probabilities is presented in the next section. For simplicity consider a choice situation with two alternatives A and B; the counter-dependent component and the random component are set to zero. As shown in Figure 3, transition probabilities are the same for the outgoing edges of each vertex v ∈ V, i.e., for each edge (v,v(A+)) ∈ E leading to a vertex with label A+, for each edge leading to a vertex with label B+ and so on for the other counters A− and B−. The probability for walking along a specific path is the product of transition probabilities of all edges on that path. In our example, the probability p for making the first three steps as shown in Figure 2 is p = p(B+)·p(A−)·p(B+).

Bottom Line: It implements pairwise comparison of alternatives on weighted attributes into an information sampling process which, in turn, results in a preference process.Then it is shown how the model accounts for several context-effects observed in human preferential choice like similarity, attraction, and compromise effects and how long it takes, on average, for the decision.A short discussion on how the 2N-ary choice tree model differs from the multi-alternative decision field theory and the leaky competing accumulator model is provided.

View Article: PubMed Central - PubMed

Affiliation: School of Humanities and Social Sciences, Jacobs University Bremen Bremen, Germany.

ABSTRACT
The 2N-ary choice tree model accounts for response times and choice probabilities in multi-alternative preferential choice. It implements pairwise comparison of alternatives on weighted attributes into an information sampling process which, in turn, results in a preference process. The model provides expected choice probabilities and response time distributions in closed form for optional and fixed stopping times. The theoretical background of the 2N-ary choice tree model is explained in detail with focus on the transition probabilities that take into account constituents of human preferences such as expectations, emotions, or socially influenced attention. Then it is shown how the model accounts for several context-effects observed in human preferential choice like similarity, attraction, and compromise effects and how long it takes, on average, for the decision. The model is extended to deal with more than three choice alternatives. A short discussion on how the 2N-ary choice tree model differs from the multi-alternative decision field theory and the leaky competing accumulator model is provided.

No MeSH data available.