Voting Behaviour Analysis

Distribution of votes against by party group

Figure 1

Distribution of vote differences by party pair

Figure 2

DEU position difference vs. vote difference

Figure 3

Ordinal betaregression

## Ordered Beta Regression Results

**Model:** `dif_vote ~ dif_DEU + (1 | procedure_reference)`  

**Family:** Ordered Beta Regression | **N =** 581 | **Chain:** 1 × 1000 post-warmup draws

	Posterior		95% CI		Convergence
Parameter	Estimate	Est.Error	l-95% CI	u-95% CI	Rhat	Bulk_ESS	Tail_ESS
Multilevel Hyperparameters
sd(Intercept)	0.49	0.10	0.33	0.72	1	318	484
Regression Coefficients
Intercept	-0.83	0.14	-1.12	-0.56	1	453	553
dif_DEU	0.01	0.00	0.00	0.01	1	1224	725
Distributional Parameters
phi	1.43	0.07	1.29	1.58	1	1002	711
cutzero	-2.74	0.16	-3.04	-2.42	1	932	692
cutone	1.87	0.06	1.76	1.99	1	1089	601
Note:
Rhat ≈ 1 indicates convergence. Bulk_ESS and Tail_ESS are effective sample size measures.

Figure 4: Table 1. Ordered Beta Regression — dif_vote ~ dif_DEU + (1 | procedure_reference), N = 581

> **Interpretation:** A higher `dif_DEU` (larger ideological distance between delegations) 

is associated with a slightly but credibly positive increase in voting divergence (β = 0.01, 

95% CI [0.00, 0.01]). The random intercept SD (0.49) suggests meaningful variation 

across legislative procedures.

Voting alignment by party pair

Figure 5

Voting alignment vs. initial position difference

Figure 6

Voting alignment vs. initial position difference by pair

Figure 7

📈 Model testing the effect of difference on the odds of voting the same way

This model estimates the relationship between ideological distance (dif_DEU) and the probability that two groups vote on the same side. A logistic mixed-effects model is used, including a random intercept for each legislative procedure (procedure_reference) to account for clustering across votes.

Odds ratios from mixed-effects logistic regression (* p < 0.05, ** p < 0.01, *** p < 0.001)

term	estimate	odds_ratio	stars
(Intercept)	3.297	27.039	***
Difference between intial positions	-0.020	0.980	***

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📈 Visualisation of the effect