Add 95% error bars to simulation examples (exact binomial + bootstrap SUE)

[endolith]

Summary

Addresses issue #13 by documenting uncertainty explicitly on the plots that estimate proportions or ratios from Monte Carlo simulation.

Accuracy relative to #13 / #14

• Issue Add uncertainty to estimates #13 correctly warns that SD, standard error, and CI are different quantities; anything plotted should be labeled. PR Add 95% CI error bars to CE and CW examples #14’s direction (explicit 95% confidence intervals for binomial counts rather than a vague “variance” bar) matches standard practice for yes/no simulation outcomes.
• Binary / count plots (Condorcet efficiency conditional on a CW existing, Condorcet paradox rate, Niemi comparison): two-sided exact (Clopper–Pearson) intervals from scipy.stats.binomtest(...).proportion_ci(method='exact'), i.e. the inverse binomial test. This is an accepted frequentist CI for a binomial proportion with fixed trial count per point.
• Social utility efficiency is not binomial; it is implemented here as the ratio of sums actually accumulated in each script: (\hat\theta=\sum_i W_i/\sum_i Z_i) with paired ((W_i,Z_i)) per simulation draw (definitions of (W,Z) match each figure: random-society baseline, spatial-model (A/B), etc.). Uncertainty uses a paired percentile bootstrap on that same ratio statistic—appropriate for the plug-in estimator being displayed.

Shared helpers and rationale live in examples/plot_uncertainty.py.

Examples updated

Plotted examples that expose a scalar estimate per (x)-value now carry asymmetric vertical intervals:

• Merrill CE / Wikipedia paradox / Niemi: binomial CIs
• Merrill Fig 3 & 4 (classic + updated), Weber effectiveness tables: bootstrap CIs for SUE

Histogram-style scripts (e.g. distributions_by_*, Tomlinson figures, Merrill Fig 2a–2b scatter) are unchanged—density/scatter visuals do not use the same single-point CI semantics.

Tests

pytest (191 tests) passes locally.

  

[codecov]

Codecov Report

✅ All modified and coverable lines are covered by tests.
✅ Project coverage is 96.31%. Comparing base (8a7213f) to head (0029212).

Additional details and impacted files

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  Lines         489      489           
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Flag	Coverage Δ
no-numba	95.50% <ø> (ø)
numba	89.16% <ø> (ø)

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