StatisticsLab

Where Do the Justices Stand: Estimating Ideal Points from Votes

Where does the axis come from when we place a justice on a scale of tendency? Using the Taiwan Constitutional Court's official per-item vote records since 2022 as real votes, this piece estimates each justice's tendency to strike down (theta) with a Bayesian graded-response model, then tests whether that axis aligns with the nominating president. Nothing is detectable on four dimensions, and the null carries power, equivalence, and specification-curve discipline; per-justice credible intervals are wide and all adjacent ones overlap, so in this sparse-dissent term the justices are mostly indistinguishable. A second layer, the co-signing network of opinions since 1949 modelled with a hierarchical binomial, does find a moderate and robust same-nominee effect. The voting layer detects nothing; the collaboration layer detects something; the two speak to different things. No prior Taiwanese study has used official per-item real votes — this piece fills that gap, and reserves its novelty claim against one closely overlapping study whose full text remains unavailable.

2026-07-19published2026-08-13updated1 min readideal points item response theory graded response model Bayesian estimation permutation test judicial behavior non-significant result

The full English version of this piece is in preparation. The finished draft is the Chinese article; this page shows the two interactive figures with English labels while the prose is being written.

This study asks whether a high-consensus constitutional court's votes can locate its justices on an ideological scale. Using the Taiwan Constitutional Court's official per-item vote records since 2022 as real votes, it estimates each justice's tendency to strike down ( $\theta$ ) with a Bayesian graded-response model, then tests whether that axis aligns with the nominating president.

colour = nominating president: 蔡英文馬英九

Each justice's tendency to vote for unconstitutionality. Left: classical MDS position, a single point. Right: Bayesian graded-response estimate with a 90% credible interval. The intervals are wide and overlap; colours (nominating president) interleave rather than clustering — justices nominated by the same president do not stand together on the merits. Bayesian GRM: 19 justices, 1388 observations, R-hat 1.0034, 0 divergent.

Nothing is detectable on four grouping dimensions, and the null carries power, equivalence, and specification-curve discipline. A second layer — the co-signing network of opinions since 1949, modelled with a hierarchical binomial — does find a moderate, robust same-nominee effect.

Each row is one algorithm setting (co-service threshold, era control, over-dispersion form). The dot is the same-nominee effect as an odds ratio, the bar its 90% credible interval. All eight sit to the right of "1× (no effect)" with lower bounds above 1 — justices nominated by the same president co-sign about 1.5× more often per shared case, and the result holds across settings. Bayesian hierarchical binomial model, 111 justices, 1144 co-serving pairs; seed 20260718.

The voting layer detects nothing; the collaboration layer detects something; the two speak to different constructs. Full text, literature analysis, and methods to follow.

answered 0 / 4

1
Two justices both dissent 40% of the time. Does this mean the measurement model will place them at nearly the same point on the ideal-point axis?
2
After ranking the 19 justices by their theta point estimates, every adjacent pair's 90% credible interval overlaps. Does this show that 'we have measured everyone to be in the middle, with no differences'?
3
The permutation test for the nominating-president dimension gives p = 0.34 (not significant). The piece also reports an MDE of 0.085 and a 90% interval bounding the effect to about ±0.1. Are these two extra numbers mainly there to make the null look richer?
4
The collaboration layer finds that same-nominee justices co-sign more often (about 1.5× the odds), while the voting layer detects no appointment politics. Is this reading correct: 'Since the collaboration layer has a signal, the voting-layer null should be revised to an effect too'?