Pith. sign in

REVIEW 3 major objections 4 minor 54 references

Ballot Design and Electoral Outcomes: The Role of Candidate Order and Party Affiliation

T0 review · 3 major / 4 minor · reviewed 2026-08-06 · deepseek-v4-flash

Challenge this review Re-run · record.json Download PDF Read on arXiv ↗

Pith's one-line read Party-order flips misled about 12–15% of NC judicial voters

desk verdict A clever natural experiment on ballot order with a strong placebo, but the headline mistake rates are boundary extrapolations of a fitted polynomial on 13 contests and should be read as model-dependent estimates, not measured facts. read the letter →

arxiv 2507.16722 v2 pith:WKC3FHB6 submitted 2025-07-22 stat.AP

Alessandro Arlotto , Alexandre Belloni , Fei Fang , Saša Pekeč This is my paper
classification stat.AP
keywords ballotdesigncausalinferencedoublemachinelearningconditionalaveragetreatmenteffectparty-orderflippartisanandnonpartisanelectionscandidateordervoterintent
verification ladder T0 review T1 audit T2 compute T3 formal

The pith

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The reading

The paper tries to establish that when a ballot mixes races with and without party labels, partisan voters use the party order in the labeled races as a cue in the unlabeled races, and that when the two orders differ they cast votes against their own intent. Using 13 North Carolina statewide judicial races without party labels from 2004–2016, it estimates that 11.8% of Democratic and 15.4% of Republican partisan voters cast incorrect judicial votes because of such a party-order flip. The estimated flip effect is heterogeneous: it helps a party's judicial candidate in precincts where that party's presidential candidate is weak and hurts them where the party is strong, so the net average effect is near zero even though mistakes are large. A placebo test on races with party labels shows the flip effect vanishes when affiliation is visible. If right, mixed-label ballots systematically misrepresent voter intent in down-ballot races.

What carries the argument

The carrying object is the flip effect $f(x)$, the conditional average treatment effect of a party-order flip on a party's judicial vote share given the presidential vote share $x$ in the same precinct. It is modeled in a partially linear outcome equation $Y = f(X)T + g(X,W,Z) + \epsilon$, with $f$ a degree-$q$ polynomial (cubic in the main results), estimated by double machine learning with cluster-robust standard errors and bootstrap uniform confidence bands. Identification of the mistake share uses the boundary value $x=1$: in a hypothetical precinct where one party receives all presidential votes, opposing-party mistakes cannot exist, so $|f(1)|$ measures the fraction of that party's partisan voters misled by the flip. The contest-level treatment assignment is argued to be quasi-randomized because the NC General Statute's ballot-order rules give each candidate roughly a 50% chance of being listed first, independent of precinct characteristics.

What would settle it

Re-estimate $|f(1)|$ using only precincts with presidential vote share above 0.9, or with candidate-name-order fixed effects added; if the fitted curve flattens or reverses at the boundary, the mistake-rate estimates are artifacts of extrapolation rather than measured voter behavior.

Watch

Extended reading notes

Core claim

The central discovery is that party-order flips are a real causal force in nonpartisan judicial races, not noise. Defining a flip as a difference between the party order of a judicial contest and the party order of the presidential race on the same ballot, the paper estimates the conditional average flip effect $f(x)$ on a party's judicial vote share given presidential vote share $x$. Using contest-level treatment assignment generated by the North Carolina statute and double machine learning on 37,690 precinct-level observations, it finds $f$ is significantly nonzero and heterogeneous, with tests rejecting both a zero flip effect and a homogeneous flip effect for each party. The share of partisan-voting mistakes, identified as $|f(1)|$, is 11.8% for Democrats and 15.4% for Republicans. In the placebo sample of races with party labels, the flip effect is indistinguishable from zero. The paper concludes that ballots mixing labeled and unlabeled contests mislead many voters and should be avoided.

Load-bearing premise

The estimate that 11.8% and 15.4% of voters were misled rests on extrapolating the fitted flip-effect curve to a hypothetical precinct where one party wins 100% of presidential votes; at that boundary every lost judicial vote is attributed to that party's own voters being fooled by the order change.

Editorial extensions

If this is right

  • A party-order flip in one unlabeled race can shift judicial vote shares by enough to matter in close elections, even when the statewide average effect is zero.
  • Analyses that only estimate an average treatment effect will miss the distortion entirely; heterogeneity across presidential vote share is necessary to see it.
  • Including party designations on all contests removes the effect, as the placebo test shows.
  • The 11.8% and 15.4% figures imply that roughly one in eight Democrats and one in seven Republicans voting in these races did not vote their intent purely because of candidate order.
  • Ballots that mix partisan and nonpartisan contests should be redesigned, since they misrepresent voter intent rather than merely shift margins.

Reading between the lines

Editorial extensions of the paper, not claims the author makes directly.

  • Beyond the paper, any state with mixed-label ballots and random or rotating candidate order could exhibit the same cue-taking; a natural extension would be re-running the same design on other states' judicial elections where party endorsements can be recovered.
  • The boundary extrapolation is the fragile link: if name-order effects or nonpartisan crossover voting operate at extreme presidential-vote-share precincts, $|f(1)|$ is not a clean mistake rate, though the qualitative conclusion that flip effects are real likely survives.
  • A sharper test of the mechanism would use individual-level ballot images or voter files to verify that voters select the candidate in the same position as their party's presidential candidate, rather than the candidate affiliated with their party.
  • The method's logic—estimating offsetting mistake shares from a heterogeneous treatment-effect curve—could transfer to other settings where agents use a visible ordering cue to infer an unlabeled attribute, such as ranked lists in retail or information displays.
Share X Bluesky LinkedIn Reddit HN

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, and a circularity audit.

Referee Report

3 major / 4 minor

Summary. The paper analyzes North Carolina statewide judicial races without party labels (2004–2016) to estimate the effect of a party-order "flip" relative to the presidential race on judicial vote shares. Using precinct-level data from 13 nonpartisan contests (6 flipped, 7 not) and a double machine learning estimator with a polynomial flip-effect function, the authors report a heterogeneous conditional flip effect and interpret the boundary value |f(1)| as the share of partisan voters who cast votes contrary to their intent, yielding 11.8% for Democratic and 15.4% for Republican voters. A placebo test using 13 judicial races with party labels finds no flip effect, and robustness checks compare cubic, linear, and constant specifications.

Significance. If the headline estimates were structurally identified, the paper would make a consequential contribution to the study of ballot design: it would show that mixing labeled and unlabeled contests can systematically distort down-ballot outcomes, with 10–15% of partisan voters potentially voting against their intent. The manuscript has real strengths: the double machine learning procedure is described in algorithmic detail, inference uses cluster-robust standard errors and uniform confidence bands, the placebo design is appropriate for testing the party-label mechanism, and the data are from public sources. However, the central interpretation of |f(1)| as a mistake rate is not derived from the identifying assumptions, and the boundary estimate is extrapolated from a global polynomial estimated on only 13 contests. Those issues are load-bearing for the main claim, so the paper needs substantive revision rather than minor polishing.

major comments (3)
  1. [Section 3.1, Eq. (1)–(2)] The identification of the share of partisan-voting mistakes as |f(1)| is asserted, not derived. The flip effect f(x) is a conditional average treatment effect on judicial vote share given presidential vote share; converting f(1) into a mistake rate requires that, in a precinct where one party receives 100% of the presidential vote, all voters are partisans of that party, that they all vote in the judicial race (no roll-off), that no independent or cross-party voters exist, and that the only behavioral response to a flip is the party-cue mistake. None of these conditions is stated as an assumption or tested. The dataset includes precinct-level party registration (Section 2.2), which could be used to measure partisan composition directly or to validate the presidential-vote-share proxy; without such validation, the headline numbers should be presented as boundary extrapolations of the flip effect, not as structural mistake rates.
  2. [Section 3.2 and Section 4.1/Table 2] The headline estimate is an extrapolation of a global polynomial to x=1, and the estimate is not stable across plausible polynomial degrees. For Republicans, the linear specification gives 11.0% while the cubic gives 15.4%; for Democrats, the linear gives 12.4% and the cubic 11.8%. The paper does not report the empirical support of the presidential vote share near 0 or 1, the number of precincts in that region, or local sensitivity analyses at the boundary. Because |f^(1)| is a linear combination of all polynomial coefficients, the paper should report support diagnostics and assess robustness using local estimates, restricted samples, or registration-based measures of partisan composition.
  3. [Section 2.2, Section 3.1, Table 1] Identification relies on contest-level treatment assignment with only 13 clusters, 6 of which are flipped. Cluster-robust standard errors with 13 clusters can understate uncertainty, and the paper reports no balance tests across flipped and non-flipped contests for contest-level characteristics such as incumbency, candidate gender, year, or race composition, even though these covariates are described as available in Section 2.2. The paper should present covariate balance and consider small-cluster corrections or randomization inference for the contest-level assignment, especially because Assumption 2 (known random assignment) is justified heuristically rather than verified for the realized set of contests.
minor comments (4)
  1. [Abstract and Section 4.1] The abstract reports 12.0% (SE 3.6%) of Democratic voters casting incorrect votes, while the main text and Table 1 report 11.8% (SE 4.0%). These numbers should be reconciled.
  2. [Section 3, Section 3.2] There are typos in the text: "stablish" in Section 3 and "hypotesis" in Section 3.2 should be corrected.
  3. [Section 4.3] The claim that the mistake shares under the linear and cubic specifications are "not statistically different from each other" is stated without reporting the test statistic or p-value; please provide the formal comparison.
  4. [Section 5 and Section 3.1] The conclusion describes the design as a "state-level treatment assignment," whereas Section 3.1 defines treatment at the contest level; this wording should be aligned for precision.

Circularity Check

0 steps flagged · score 0.0 of 10

No significant circularity: the headline mistake shares are estimates of an explicitly defined functional of the fitted flip-effect curve, not separate predictions secretly derived from the same fitted coefficients.

full rationale

The paper's central quantities are the flip-effect curve f(x), estimated from Eq. (1)-(2) by double machine learning, and the share of partisan-voting mistakes, defined in Section 3.1 as |f(1)| under the explicit (if strong) identifying assumption that at a hypothetical precinct where one party receives all presidential votes there are no opposing-party voters. Section 3.2 then states 'our point estimate for the fraction of partisan-voting mistakes is given by |f̂(1)|'. The 11.8% and 15.4% figures are therefore estimates of this estimand, not independent predictions smuggled in from the same fit; any estimate is a function of fitted coefficients, and the paper is transparent that the estimand is identified only through the boundary assumption. The paper even flags the identification problem itself: 'This estimand ... could face an identification problem since we only observe the net effect on each outcome.' The placebo test using party-labeled races provides independent, out-of-sample support for the mechanism (the flip effect disappears). There are no load-bearing self-citations; the DML methodology is cited from standard external literature. Concerns about extrapolating a global polynomial to x=1, thin support at the boundary, and the use of presidential vote share rather than party registration are substantive threats to identification and external validity, but they are not circularity: the derivation does not assume the conclusion it claims to establish.

Assumptions & free parameters 3 free parameters · 5 assumptions · 0 invented entities

The central estimate is a fitted cubic curve evaluated at x=1, resting on a handful of identifying assumptions and modeling choices. No new theoretical entities are introduced.

free parameters (3)
  • Polynomial degree q of the flip effect = 3 (cubic; also 1 and 0 in robustness checks)
    Chosen by hand to allow non-monotonic and asymmetric conditional effects; higher-order terms are not significant in Table 1.
  • Democratic flip-effect polynomial coefficients theta_d0 through theta_d3 = 0.135, -0.392, 0.255, -0.117
    Fitted by double machine learning and reported in Table 1; the partisan-voting mistake estimate 11.8% is |sum of these coefficients|.
  • Republican flip-effect polynomial coefficients theta_r0 through theta_r3 = 0.116, -0.247, 0.165, -0.188
    Fitted by double machine learning and reported in Table 1; 15.4% is |sum of these coefficients|.
assumptions (5)
  • domain assumption No interference among units (Assumption 1): potential vote shares of a contest depend only on that contest's treatment.
    Standard SUTVA used to write Equation 1; plausible but untestable, and contest-level treatments could interact through shared ballot layouts.
  • domain assumption Known random assignment (Assumption 2): party-order flips are as-if randomly assigned by the legal ordering mechanism.
    The paper argues any two last names give a 50% flip chance, but candidate names are not drawn at random and no balance test is provided.
  • domain assumption Party affiliations of unlabeled judicial candidates are correctly inferred from contemporaneous endorsements.
    Section 2.2 says party affiliation is determined from endorsements; misclassification would directly mislabel the treatment T_c.
  • ad hoc to paper The flip effect f(x) is a polynomial of degree q in presidential vote share.
    Equation 2 imposes the functional form; robustness to linear and constant specifications is checked, but the true form is unknown.
  • ad hoc to paper At x=1, the flip effect identifies the share of partisan-voting mistakes because no opposing-party voters exist to cancel mistakes.
    Section 3.1 defines the estimand via hypothetical 100% precincts; extrapolation of the fitted curve to the boundary is load-bearing.

how reviews work

0 comments
Cite this review

Pith. "Pith review of Ballot Design and Electoral Outcomes: The Role of Candidate Order and Party Affiliation." pith.science (2026). https://pith.science/paper/WKC3FHB6

@misc{pith2026250716722,
  author       = {Pith},
  title        = {Pith review of: Ballot Design and Electoral Outcomes: The Role of Candidate Order and Party Affiliation},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/WKC3FHB6}},
  note         = {Machine review of arXiv:2507.16722}
}
read the original abstract

We develop a causal inference model to study how designing ballots with and without party designations impacts electoral outcomes when partisan voters rely on party-order cues to infer candidate affiliation in races without designations. If the party orders of candidates in races with and without party designations differ, these voters might cast their votes incorrectly. We identify a quasi-randomized natural experiment with contest-level treatment assignment pertaining to North Carolina judicial elections and leverage double machine learning to accurately capture the magnitude of such incorrectly cast votes. Using precinct-level election and demographic data, we estimate that 12.0% (SE: 3.6%) of Democratic partisan voters and 15.4% (SE: 4.0%) of Republican partisan voters cast their votes incorrectly due to the difference in party orders. A placebo test using judicial races with party designations shows that the flip effect disappears when party affiliation is observable on the ballot, which is consistent with the proposed causal mechanism.

Discussion (0). Sign in to comment.

Reference graph

Works this paper leans on

54 extracted references · 54 canonical work pages

  1. [1]

    The Review of Economic Studies 83(2):460--480

    Augenblick N, Nicholson S (2015) Ballot position, choice fatigue, and voter behaviour . The Review of Economic Studies 83(2):460--480

    work page 2015

  2. [2]

    Multiscale Modeling & Simulation 19(4):1885--1914

    Autry EA, Carter D, Herschlag GJ, Hunter Z, Mattingly JC (2021) Metropolized multiscale forest recombination for redistricting. Multiscale Modeling & Simulation 19(4):1885--1914

    work page 2021

  3. [3]

    American Journal of Political Science 44(1):35--50

    Bartels LM (2000) Partisanship and voting behavior, 1952-1996. American Journal of Political Science 44(1):35--50

    work page 2000

  4. [4]

    Operations Research forthcoming

    Belotti P, Buchanan A, Ezazipour S (2025) Political districting to optimize the P olsby- P opper compactness score with application to voting rights. Operations Research forthcoming

    work page 2025

  5. [5]

    Notices of the AMS 64(9):1020--1024

    Bernstein M, Duchin M (2017) A formula goes to court: Partisan gerrymandering and the efficiency gap. Notices of the AMS 64(9):1020--1024

    work page 2017

  6. [6]

    Political Behavior 37(1):43--66

    Bonneau CW, Cann DM (2015) Party identification and vote choice in partisan and nonpartisan elections. Political Behavior 37(1):43--66

    work page 2015

  7. [7]

    Comparative Politics 44(4):403--420

    Brader T, Tucker JA (2012) Following the party's lead: Party cues, policy opinion, and the power of partisanship in three multiparty systems. Comparative Politics 44(4):403--420

    work page 2012

  8. [8]

    Management Science 68(9):6687--6696

    Cachon GP, Kaaua D (2022) Serving democracy: Evidence of voting resource disparity in F lorida. Management Science 68(9):6687--6696

    work page 2022

Show all 54 references
  1. [9]

    Journal of human resources 50(2):317--372

    Cameron AC, Miller DL (2015) A practitioner’s guide to cluster-robust inference. Journal of human resources 50(2):317--372

    2015

  2. [10]

    The Econometrics Journal 21(1):C1--C68

    Chernozhukov V, Chetverikov D, Demirer M, Duflo E, Hansen C, Newey W, Robins J (2018 a ) Double/debiased machine learning for treatment and structural parameters. The Econometrics Journal 21(1):C1--C68

    2018

  3. [11]

    Technical report, National Bureau of Economic Research

    Chernozhukov V, Demirer M, Duflo E, Fernandez-Val I (2018 b ) Generic machine learning inference on heterogeneous treatment effects in randomized experiments, with an application to immunization in I ndia. Technical report, National Bureau of Economic Research

    2018

  4. [12]

    Journal of Business & Economic Statistics 40(3):1046--1056

    Chiang HD, Kato K, Ma Y, Sasaki Y (2022) Multiway cluster robust double/debiased machine learning. Journal of Business & Economic Statistics 40(3):1046--1056

    2022

  5. [13]

    H ouse elections grow? American Journal of Political Science 40(2):478--497

    Cox GW, Katz JN (1996) Why did the incumbency advantage in U.S. H ouse elections grow? American Journal of Political Science 40(2):478--497

    1996

  6. [14]

    Cox GW, Morgenstern S (1993) The increasing advantage of incumbency in the U.S. states. Legislative Studies Quarterly 18(4):495--514

    1993

  7. [15]

    Operations Research 73(1):61--85

    Crimmins BL, Halderman JA, Sturt B (2025) Improving the security of U nited S tates elections with robust optimization. Operations Research 73(1):61--85

    2025

  8. [16]

    Harvard Data Science Review 3(1):3

    DeFord D, Duchin M, Solomon J (2021) Recombination: A family of M arkov chains for redistricting. Harvard Data Science Review 3(1):3

    2021

  9. [17]

    Law & Society Review 18(3):395--436

    Dubois PL (1984) Voting cues in nonpartisan trial court elections: A multivariate assessment. Law & Society Review 18(3):395--436

    1984

  10. [18]

    Political Participation and American Democracy 92:171--191

    Engstrom RL, Caridas VM (1991) Voting for judges: Race and roll-off in judicial elections. Political Participation and American Democracy 92:171--191

    1991

  11. [19]

    Political Behavior 24:93--115

    Fiorina MP (2002) Parties and partisanship: A 40-year retrospective. Political Behavior 24:93--115

    2002

  12. [20]

    Fiorina MP (2017) Unstable majorities: Polarization, party sorting, and political stalemate (Hoover Press)

    2017

  13. [21]

    Interfaces 39(5):443--459

    Fry MJ, Ohlmann JW (2009) Route design for delivery of voting machines in H amilton C ounty, O hio. Interfaces 39(5):443--459

    2009

  14. [22]

    Statistics and Public Policy 8(1):67--72

    Gelman A (2021) Failure and success in political polling and election forecasting. Statistics and Public Policy 8(1):67--72

    2021

  15. [23]

    Judgment and Decision Making 15(5):863–880

    Gelman A, Hullman J, Wlezien C, Elliott Morris G (2020) Information, incentives, and goals in election forecasts. Judgment and Decision Making 15(5):863–880

    2020

  16. [24]

    American Journal of Political Science 34(4):1142--1164

    Gelman A, King G (1990) Estimating incumbency advantage without bias. American Journal of Political Science 34(4):1142--1164

    1990

  17. [25]

    American Political Science Review 88(3):541--559

    Gelman A, King G (1994) Enhancing democracy through legislative redistricting. American Political Science Review 88(3):541--559

    1994

  18. [26]

    Work in progress

    Glasserman P, Kou S (2025) An endogenous equilibrium poll method to mitigate non-voting bias. Work in progress

    2025

  19. [27]

    Management Science 69(1):220--243

    Gordon BR, Lovett MJ, Luo B, Reeder JC (2023) Disentangling the effects of ad tone on voter turnout and candidate choice in presidential elections. Management Science 69(1):220--243

    2023

  20. [28]

    Proceedings of the 2021 SIAM Conference on Applied and Computational Discrete Algorithms (ACDA21), 88--99

    Gurnee W, Shmoys DB (2021) Fairmandering: A column generation heuristic for fairness-optimized political districting. Proceedings of the 2021 SIAM Conference on Applied and Computational Discrete Algorithms (ACDA21), 88--99

    2021

  21. [29]

    ar X iv 2410.13900

    Haseltine CA, Albert LA (2024) Voting by mail: A M arkov chain model for managing the security risks of election systems. ar X iv 2410.13900

    2024 arXiv

  22. [30]

    Operations Research 13(6):998--1006

    Hess SW, Weaver J, Siegfeldt H, Whelan J, Zitlau P (1965) Nonpartisan political redistricting by computer. Operations Research 13(6):998--1006

    1965

  23. [31]

    Journal of the American Statistical Association 101(475):888--900

    Ho DE, Imai K (2006) Randomization inference with natural experiments: An analysis of ballot effects in the 2003 C alifornia recall election. Journal of the American Statistical Association 101(475):888--900

    2006

  24. [32]

    Public Opinion Quarterly 72(2):216--240

    Ho DE, Imai K (2008) Estimating causal effects of ballot order from a randomized natural experiment: The C alifornia alphabet lottery, 1978–2002 . Public Opinion Quarterly 72(2):216--240

    2008

  25. [33]

    King A, Leigh A (2009) Are ballot order effects heterogeneous? Social Science Quarterly 90(1):71--87

    2009

  26. [34]

    H ouse elections

    King G, Gelman A (1991) Systemic consequences of incumbency advantage in U.S. H ouse elections. American Journal of Political Science 35(1):110--138

    1991

  27. [35]

    The Journal of Politics 66(1):267--281

    Koppell JG, Steen JA (2004) The effects of ballot position on election outcomes. The Journal of Politics 66(1):267--281

    2004

  28. [36]

    American Journal of Political Science 41:270--283

    McDermott ML (1997) Voting cues in low-information elections: Candidate gender as a social information variable in contemporary U nited S tates elections. American Journal of Political Science 41:270--283

    1997

  29. [37]

    The Journal of Politics 67(1):201--219

    McDermott ML (2005) Candidate occupations and voter information shortcuts. The Journal of Politics 67(1):201--219

    2005

  30. [38]

    Political Behavior 35:175--197

    Meredith M, Salant Y (2013) On the causes and consequences of ballot order effects. Political Behavior 35:175--197

    2013

  31. [39]

    The Public Opinion Quarterly 62(3):291--330

    Miller JM, Krosnick JA (1998) The impact of candidate name order on election outcomes. The Public Opinion Quarterly 62(3):291--330

    1998

  32. [40]

    33rd Conference on Neural Information Processing Systems, Vancouver, Canada, 6

    Oprescu M, Syrgkanis V, Battocchi K, Hei M, Lewis G (2019) Econ ML : A machine learning library for estimating heterogeneous treatment effects. 33rd Conference on Neural Information Processing Systems, Vancouver, Canada, 6

    2019

  33. [41]

    Journal of Consumer Research 34(6):794--806

    Phillips JM, Urbany JE, Reynolds TJ (2008) Confirmation and the effects of valenced political advertising: A field experiment. Journal of Consumer Research 34(6):794--806

    2008

  34. [42]

    IISE Transactions 56(4):424--436

    Schmidt A, Albert LA (2024) The drop box location problem. IISE Transactions 56(4):424--436

    2024

  35. [43]

    Manufacturing & Service Operations Management 26(3):1028--1042

    Schmidt AP, Buell D, Albert LA (2024) Optimal consolidation of polling locations. Manufacturing & Service Operations Management 26(3):1028--1042

    2024

  36. [44]

    Operations Research 73(2):752--774

    Shahmizad M, Buchanan A (2025) Political districting to minimize county splits. Operations Research 73(2):752--774

    2025

  37. [45]

    Journal of the American Statistical Association 113(522):607--614

    Shirani-Mehr H, Rothschild D, Goel S, Gelman A (2018) Disentangling bias and variance in election polls. Journal of the American Statistical Association 113(522):607--614

    2018

  38. [46]

    Nature 408(6813):665--666

    Sinclair RC, Mark MM, Moore SE, Lavis CA, Soldat AS (2000) An electoral butterfly effect. Nature 408(6813):665--666

    2000

  39. [47]

    Statistical Science 17(4):441--457

    Smith RL (2002) A statistical assessment of B uchanan's vote in P alm B each C ounty. Statistical Science 17(4):441--457

    2002

  40. [48]

    Operations Research 71(2):536--562

    Swamy R, King DM, Jacobson SH (2023) Multiobjective optimization for politically fair districting: A scalable multilevel approach. Operations Research 71(2):536--562

    2023

  41. [49]

    Operations Research 70(2):867--892

    Validi H, Buchanan A, Lykhovyd E (2022) Imposing contiguity constraints in political districting models. Operations Research 70(2):867--892

    2022

  42. [50]

    Social Science Quarterly 74:664--673

    Vanderleeuw JM, Utter GH (1993) Voter roll-off and the electoral context: A test of two theses. Social Science Quarterly 74:664--673

    1993

  43. [51]

    Statistics in Medicine 27(11):1934--1943

    VanderWeele TJ (2008) Ignorability and stability assumptions in neighborhood effects research. Statistics in Medicine 27(11):1934--1943

    2008

  44. [52]

    San Diego Union-Tribune G--3, November 19

    Wand JN, Herron MC, Brady HE (2000) Ballot cost G ore thousands of votes. San Diego Union-Tribune G--3, November 19

    2000

  45. [53]

    American Political Science Review 95(4):793--810

    Wand JN, Shotts KW, Sekhon JS, Mebane WR, Herron MC, Brady HE (2001) The butterfly did it: The aberrant vote for B uchanan in P alm B each C ounty, F lorida. American Political Science Review 95(4):793--810

    2001

  46. [54]

    Marketing Science 37(3):333--355

    Wang Y, Lewis M, Schweidel DA (2018) A border strategy analysis of ad source and message tone in senatorial campaigns. Marketing Science 37(3):333--355

    2018

Pith tools

Reviewed August 6, 2026 · model on record in the stance chip above.