<p>In politics your best move depends on what others do, and theirs on what you will do. This paper studies that interdependence in a model of distributive legislative voting: Each member of an <InlineEquation ID="IEq1"> <EquationSource Format="TEX">\(N\)</EquationSource> <EquationSource Format="MATHML"><math> <mi>N</mi> </math></EquationSource> </InlineEquation>-member legislature decides, simultaneously and without knowing how the others will vote, whether to join a winning coalition for a spending bill. Because a legislator wants to join only if the coalition is not “too” large, her vote depends on her forecast of the Yes-total. I model that forecast explicitly: Each legislator has a small random set of <i>predictors</i>—algorithms mapping past vote totals to a forecast—monitors their performance and uses her most accurate one. In simulation, the aggregate settles into a stable band around the threshold (<InlineEquation ID="IEq2"> <EquationSource Format="TEX">\(n^{*}=85\)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mmultiscripts> <mi>n</mi> <mrow /> <mrow> <mrow /> <mo>∗</mo> </mrow> </mmultiscripts> <mo>=</mo> <mn>85</mn> </mrow> </math></EquationSource> </InlineEquation> of 101), while individual legislators churn constantly beneath it, switching votes and predictors. The focal point is robust to the choice of predictors, loss function, monitoring window, and learning rule. An extended specification, where legislators also dislike backing a failing bill, supports an all-No equilibrium, exact-<InlineEquation ID="IEq3"> <EquationSource Format="TEX">\(n^{*}\)</EquationSource> <EquationSource Format="MATHML"><math> <mmultiscripts> <mi>n</mi> <mrow /> <mrow> <mrow /> <mo>∗</mo> </mrow> </mmultiscripts> </math></EquationSource> </InlineEquation> coalitions, and a fragile two-period cycle, all selected by the inherited voting history. Disagreement among rational agents who cannot take common knowledge for granted is not only sensible but a source of rich, computable structure.</p>

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Voting and expectations: a computer-simulation study of interdependent forecasting in a legislative coalition game

  • David Kane

摘要

In politics your best move depends on what others do, and theirs on what you will do. This paper studies that interdependence in a model of distributive legislative voting: Each member of an \(N\) N -member legislature decides, simultaneously and without knowing how the others will vote, whether to join a winning coalition for a spending bill. Because a legislator wants to join only if the coalition is not “too” large, her vote depends on her forecast of the Yes-total. I model that forecast explicitly: Each legislator has a small random set of predictors—algorithms mapping past vote totals to a forecast—monitors their performance and uses her most accurate one. In simulation, the aggregate settles into a stable band around the threshold ( \(n^{*}=85\) n = 85 of 101), while individual legislators churn constantly beneath it, switching votes and predictors. The focal point is robust to the choice of predictors, loss function, monitoring window, and learning rule. An extended specification, where legislators also dislike backing a failing bill, supports an all-No equilibrium, exact- \(n^{*}\) n coalitions, and a fragile two-period cycle, all selected by the inherited voting history. Disagreement among rational agents who cannot take common knowledge for granted is not only sensible but a source of rich, computable structure.