merrill_1984_table_2 and table_4 don't reproduce the published Merrill (1984) tables #88

Problem

examples/merrill_1984_table_2.py and examples/merrill_1984_table_4.py produce Condorcet/social-utility efficiencies that deviate from the published Merrill (1984) tables by more than Monte Carlo error.

Measured at 3,000 elections (a single run, so ~1 pp MC noise is included):

Table 2 (Condorcet efficiencies, 201 voters, 5 candidates) — max deviations per method:

Method	max deviation from paper (pp)
Hare	4.9
Approval	4.5
Plurality	4.4
Coombs	3.9
Runoff	3.8
SU max	3.3
Borda	2.0

Table 4 (social-utility efficiencies, 201 voters, 5 candidates) — max deviations per method:

Method	max deviation from paper (pp)
Plurality	8.9
Hare	7.5
Runoff	6.9
Coombs	3.1

For example, Table 4 Plurality at (disp 1.0, corr 0.5, D=2) is ~73 in the script vs 64 in the paper, and at (disp 0.5, corr 0.5, D=2) is ~4 vs −1.

Note the paper's Table 4 also has negative efficiencies (e.g. Plurality −1, 0), which the script's model never produces.

Impact

The new example-script tests (PR #87) therefore check these two scripts against their docstring "Typical result" tables rather than the paper values, with a note. Table 1, Table 3, and the Weber scripts do reproduce the papers within ~2 pp and are checked against the papers.

Possible causes (unverified)

• Tie-breaking or normalization differences (e.g. the paper's "Plurality*" asterisk in Table 4).
• The random-society vs spatial-model handling of utilities.

Reference

Merrill, S. (1984). "A Comparison of Efficiency of Multicandidate Electoral Systems." American Journal of Political Science 28(1), 23-48.