Pith Number

pith:ZGUWW2KW

pith:2026:ZGUWW2KWWRGGYCWH4EOS7HTAQF

not attested not anchored not stored refs resolved

Ballot Exhaustion in Multiwinner Single Transferable Vote Elections

David McCune, E.E. Naber

Raw ballot exhaustion rates in multiwinner STV overstate how often voters lose representation.

arxiv:2605.12676 v1 · 2026-05-12 · econ.GN · q-fin.EC

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\usepackage{pith}
\pithnumber{ZGUWW2KWWRGGYCWH4EOS7HTAQF}

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Record completeness

1 Bitcoin timestamp

2 Internet Archive

3 Author claim open · sign in to claim

4 Citations open

5 Replications open

✓ Portable graph bundle live · download bundle · merged state

The bundle contains the canonical record plus signed events. A mirror can host it anywhere and recompute the same current state with the deterministic merge algorithm.

Claims

C1strongest claim

raw exhaustion rates alone substantially overstate the extent to which voters lose their influence or fail to obtain representation under STV.

C2weakest assumption

The proportional ballot-completion model accurately reflects how voters would complete their ballots if given more options.

C3one line summary

27.9% of ballots exhaust in Scottish STV elections but weight exhaustion is only 7.1%, and most voters still achieve representation.

References

23 extracted · 23 resolved · 0 Pith anchors

[1] T. Bardal, M. Brill, D. McCune, & J. Peters. (2024). Proportional Representation in Practice: Quantifying Proportionality in Ordinal Elections.Proceedings of the AAAI Conference on Artificial Intellig 2024

[2] G. Benad` e, C. Donnay, M. Duchin, and T. Weighill. (2024) Proportionality for ranked voting, in theory and practice. Preprint:https://mggg.org/PRVTP 2024

[3] C.M. Burnett & V. Kogan. (2015). Ballot (and voter) “exhaustion” under Instant Runoff Voting: An examination of four ranked-choice elections.Electoral Studies37: 41-49 2015

[4] A. Clark. (2013). Second time lucky? The continuing adaptation of voters and parties to the single transferable vote in Scotland.Representation49(1): 55-68 2013

[5] A. Clark. (2021). The effects of electoral reform on party campaigns, voters and party systems at the local level: from single member plurality to the single transferable vote in Scotland.Local Govern 2021

Formal links

1 machine-checked theorem link

Receipt and verification

First computed	2026-05-18T03:09:50.063323Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

c9a96b6956b44c6c0ac7e11d2f9e6081518215172557bc46ebf7964d069a678e

Aliases

arxiv: 2605.12676 · arxiv_version: 2605.12676v1 · doi: 10.48550/arxiv.2605.12676 · pith_short_12: ZGUWW2KWWRGG · pith_short_16: ZGUWW2KWWRGGYCWH · pith_short_8: ZGUWW2KW

Agent API

Resolver JSON Graph JSON Events JSON Schema Signing key

Verify this Pith Number yourself

curl -sH 'Accept: application/ld+json' https://pith.science/pith/ZGUWW2KWWRGGYCWH4EOS7HTAQF \
  | jq -c '.canonical_record' \
  | python3 -c "import sys,json,hashlib; b=json.dumps(json.loads(sys.stdin.read()), sort_keys=True, separators=(',',':'), ensure_ascii=False).encode(); print(hashlib.sha256(b).hexdigest())"
# expect: c9a96b6956b44c6c0ac7e11d2f9e6081518215172557bc46ebf7964d069a678e

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "58fda8616b13929218fd8a7060021e65c96d6ba36d50a382b8e1d3c488a3de10",
    "cross_cats_sorted": [
      "q-fin.EC"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "econ.GN",
    "submitted_at": "2026-05-12T19:26:40Z",
    "title_canon_sha256": "49390eb26c15c356059d99353a265737d159a6fbbf390125f28e54ad6bb644e4"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2605.12676",
    "kind": "arxiv",
    "version": 1
  }
}