The calculus of democratic deliberation

Abstract

Deliberation may increase the quality of decisions but also necessarily takes time and effort and hence will have costs. But proponents of deliberative democracy as an attractive or superior method for making decisions almost all focus on presumed benefits while in practice ignoring the costs associated with investing time and resources in the process of deliberation. We show that the cost side significantly influences the performance of the deliberative process. Through a number of simulations, we demonstrate that there must be a certain point beyond which the costs of deliberating will outweigh the potential benefits. Since this type of processes invariably will be time consuming, especially when the convergence of the participants towards a common goal is slow, conditions are derived where the deliberative process performs relatively well or relatively poorly, both as concerns the probability of reaching an agreement and in the net benefits to the participants. This is especially the case when the number of participants increase.

Appendix

For all calculations, (if nothing else is mentioned) we use the following parameter values: $U_{i} \left( {C_{t} } \right) = U\left( C \right) = 30$, $\beta_{it} = \beta = 1$, $a_{0} = 5$, $a_{1} = 0.5$, $TC_{i} = 2$, $n = 3$. Start value = 5% (implying that $P_{i1} = \left( {P_{0}^{A} - P_{i0} } \right)\cdot5\% + P_{i0}$) 3 participants with initial position: $P_{1}^{I} = 1$, $P_{2}^{I} = 3$, $P_{3}^{I} = 8$.

1.1 Additional material for Sect. 3

See Table 2.

Table 2 Effect of changes in one parameter on the performance of the deliberation process

Increasing $n$ is done by duplicating the participants from the original situation (which means $P_{1}^{I} = P_{4}^{I} , P_{2}^{I} = P_{5}^{I}$ and $P_{3}^{I} = P_{6}^{I}$). Thereby the group variance is unchanged, while $\frac{{\partial V_{t}^{e} }}{{\partial P_{it} }}$ is halved and the result holds that for $n = 6$, no consensus exists (Table 3).

Table 3 Effect of changing an individual $\alpha_{it}$ on outcome of deliberative process

Note that an increase in $\alpha_{3t}$ by 25%, results in a decrease in all participants position changes, reduces the probability of consensus and reduces all participants expected net benefits. A reduction in $\alpha_{3t}$ gives the opposite result. Remarkably, all participants benefit almost identically even though only $\alpha_{3t}$ is subject to the change (Table 4).

Table 4 Effect of changing an individual ${\varvec{U}}_{{\varvec{i}}} \left( {\varvec{C}} \right)$ on outcome of deliberative process

Note that changes in $TC_{i}$ does not affect the optimal choice of position in a round but might affect how many rounds are optimal for that participant, and thereby reduces the probability of consensus. Changes in ${\varvec{U}}_{{\varvec{i}}} \left( {\varvec{C}} \right)$ does affect both the optimal choice of position in any round and the utility for that participant. A sufficiently increase in $U_{3} \left( C \right)$, makes positions converge faster and increase the net benefit for all participants. A sufficiently decrease in ${\varvec{U}}_{3} \left( C \right)$ reducing utility for all participants.

1.2 Additional material for Sect. 4

The effect of preference change on performance of deliberative process.

In this example, we model preference shifts as follows:

$$P_{it}^{ \cdot } = P_{i}^{I} \cdot \left( {1 + z} \right)^{t} + \frac{1}{{2\alpha_{it} }}\left( {\frac{{dPr_{t}^{E} }}{{dV_{t} }} \cdot U_{i} \left( {C_{t} } \right) + \beta_{i} } \right) \cdot \left( { - \frac{{\partial V_{t}^{E} }}{{\partial P_{it} }}} \right),\;\;{\text{if}}\;\;\frac{{\partial V_{t}^{E} }}{{\partial P_{it} }} < 0\left( {P_{it} < P_{t}^{A} } \right)$$

$$P_{it}^{*} = P_{i}^{I} \cdot \left( {1 - z} \right)^{t} - \frac{1}{{2\alpha_{it} }}\left( {\frac{{dPr_{t}^{E} }}{{dV_{t} }} \cdot U_{i} \left( {C_{t} } \right) + \beta_{i} } \right) \cdot \left( { - \frac{{\partial V_{t}^{E} }}{{\partial P_{it} }}} \right),\;\;{\text{if}}\;\;\frac{{\partial V_{t}^{E} }}{{\partial P_{it} }} > 0\left( {P_{it} > P_{t}^{A} } \right)$$

Hence, for any given period, we let the initial position be moved towards the average position by a factor of $\left( {1 \pm z} \right)^{t}$. Results presented in Table 5.

Table 5 Effect of preference change on performance of deliberative process