Voting

Principled social-choice aggregation as MCP tools — with a benchmark that measures the accuracy lift over naive majority vote.

Almost every multi-agent system aggregates votes with Counter(votes).most_common(1), throwing away preference order and confidence. voting-mcp ships the real rules (Borda, Copeland, Condorcet, approval, STV, linear opinion pool) as callable MCP tools — each with its known axiomatic behavior and explicit, documented tie-breaking — plus a reproducible benchmark that aggregates a diverse ensemble of LLMs on a reasoning set and reports accuracy with bootstrap confidence intervals.

The server is pure compute: stdio transport, no network, no file writes, no secrets — clean against the OWASP MCP Top 10 by construction.

Install

# run the server directly (once published)
uvx voting-mcp

# or from source
git clone https://github.com/HrishiKabra/voting-mcp && cd voting-mcp
uv sync
uv run python -m voting_mcp.server

Add it to an MCP client (e.g. Claude Desktop claude_desktop_config.json):

{
  "mcpServers": {
    "voting": { "command": "uvx", "args": ["voting-mcp"] }
  }
}

Tools

Every tool takes a profile ({candidates, ballots}) and returns a Result with the full co-winner set (winners, so ties are never hidden), the single tie-broken winner (or null when none exists), a ranking, per-candidate scores, and a note.

Tool	Ballots	Notes
borda	rankings	positional; Condorcet-inconsistent, clone-sensitive
copeland	rankings	Condorcet-consistent pairwise (+1 win, +0.5 tie)
condorcet	rankings	returns the pairwise winner or an explicit no-winner on a cycle
approval	approval sets	most-approved wins
stv	rankings	single-winner instant-runoff; clone-resistant
opinion_pool	distributions	linear pool — preserves confidence, not an argmax vote
plurality	rankings	baseline (most first choices)
majority	rankings	strict >50% or no winner
aggregate_rule	any	dispatch by a rule enum

Tie-breaking is an explicit parameter (lexicographic default, none, or seeded random).

Benchmark

Aggregate an ensemble of 5 models (one OpenAI-compatible client via OpenRouter) on ARC-Challenge and compare each rule to the naive majority vote:

uv sync --extra bench
uv run python -m bench.fetch_arc --limit 200
# prints a cost estimate and STOPS; add --yes to actually call the API, --mock for a free dry run
uv run python -m bench.run_ensemble --dataset bench/datasets/arc_challenge.jsonl --limit 200 --yes
uv run python -m bench.compare --dataset bench/datasets/arc_challenge.jsonl --limit 200

Every raw response is cached under bench/results/raw/; re-runs never re-call the API, so aggregation tweaks are free.

Results

5-model ensemble (gpt-4o-mini · gemini-2.5-flash-lite · deepseek-v3 · claude-haiku-4.5 · glm-4.7), n = 200, bootstrap 95% CI. Two datasets of different difficulty; full write-up and both plots in RESULTS.md.

MMLU-Pro (hard, baseline 73.5%) — the informative case:

Rule	Accuracy	95% CI	paired Δ vs majority	p
opinion_pool	0.755	[0.695, 0.815]	+0.020 [−0.011, +0.052]	0.225
majority_vote (baseline)	0.735	[0.679, 0.788]	—	—
approval	0.701	[0.640, 0.757]	−0.035 [−0.063, −0.006]	0.014
stv	0.693	[0.630, 0.750]	−0.043 [−0.072, −0.015]	0.002
copeland	0.647	[0.580, 0.710]	−0.088 [−0.127, −0.052]	<0.001
condorcet	0.620	[0.550, 0.685]	−0.115 [−0.155, −0.079]	<0.001
majority (strict)	0.590	[0.520, 0.655]	−0.145 [−0.189, −0.105]	<0.001
borda	0.472	[0.405, 0.540]	−0.263 [−0.323, −0.206]	<0.001

Δ is tested with a paired bootstrap on the per-question accuracy difference (same questions, so shared difficulty cancels), not by eyeballing the independent CIs.

The finding (honest): the value isn't "fancy voting beats majority." It's that the confidence-preserving rule (opinion_pool) wins when the crowd is uncertain (+2.0pp, the only rule above baseline — suggestive but not significant at n=200, paired p=0.225), while forcing the distributions into full rankings actively hurts, significantly — every ranking rule is below baseline at paired p≤0.014, and borda collapses to 0.472 because with 10 options the tail of the ranking is mostly noise. Aggregate the confidence; don't throw it away. On ARC-Challenge (baseline 96.8%, near-ceiling) nothing separates — no rule differs significantly. See RESULTS.md.

Develop

uv run pytest -q
uv run ruff check .
uv run mypy --strict src
# exercise the tools in the MCP Inspector:
npx @modelcontextprotocol/inspector uv run python -m voting_mcp.server

Note: if you keep this repo under an iCloud-synced folder (e.g. ~/Desktop), iCloud can spawn duplicate .pth files that intermittently break the editable install. Tests use pythonpath=src; run the server with PYTHONPATH=src if an import fails, or move the repo off the synced folder.

Related research

The choice of rules here grows out of the author's work on voting-rule design: Optimizing Voting Rules for Social Welfare and Beyond (AAMAS). That line of work asks which aggregation rules maximize welfare given how voters actually express preferences; this project applies the same lens to LLM ensembles — where the benchmark's answer is that confidence-preserving aggregation (the linear opinion pool) is what pays off, and forcing cardinal beliefs into ordinal rankings destroys signal.

License

MIT