Multi-Round Accumulative Voting (MAV)

Updated 4 July 2026

MAV is a voting mechanism where support is aggregated over multiple rounds, allowing earlier votes to carry over to the final tally.
It is applied in diverse contexts, from electoral systems that combine votes across rounds to structured generation processes in machine learning.
MAV designs involve iterative, staged aggregation with varying state-transition rules, influencing fairness, strategic behavior, and computational efficiency.

Searching arXiv for the cited works and closely related MAV material. Multi-Round Accumulative Voting (MAV) designates a class of procedures in which support is expressed, revealed, or computed over more than one round and the final outcome depends on accumulation rather than replacement of earlier rounds. In the available arXiv literature, the term is used most directly in two rather different settings: electoral procedure design, where round-by-round votes are added into a final tally, and inference-time aggregation for structured generation, where repeated model outputs are counted until one candidate becomes sufficiently dominant (Hart, 2022, Wang et al., 24 Jul 2025). Taken together, the literature suggests that MAV is not a single settled formalism but a family of additive, staged, and iterative aggregation mechanisms whose exact semantics depend on what is carried across rounds: vote totals, survivor sets, thresholds, set-valued local states, ranked support, or transferable cumulative vote mass.

1. Terminological scope and core architectures

The literature separates several distinct architectures that are relevant to MAV.

Domain	Representative papers	What accumulates
Electoral two-round voting	(Hart, 2022, Gersbach et al., 2017)	Votes from earlier rounds remain in the final tally
Structured generation	(Wang et al., 24 Jul 2025)	Frequencies of repeated generated triplets
Related staged or iterative models	(Gong et al., 2024, Malafeyev et al., 2017, Salehkaleybar et al., 2017, Grama, 2021, Skowron et al., 2020)	Survivor sets, thresholds, set-valued states, ranked support, or transferred vote mass

A central distinction in this literature is between accumulative procedures and reset or runoff procedures. The two-round electoral proposal in "Repeat Voting" is explicitly accumulative because the first-round votes remain part of the final tally; it is therefore “not a conventional two-round runoff in which only the second-round vote decides” (Hart, 2022). By contrast, the unified multi-stage multi-winner framework carries only the surviving candidate set from one stage to the next and explicitly has “no score carryover variable,” so it is multi-stage without being accumulative in the literal tally-addition sense (Gong et al., 2024). The threshold-elimination game likewise re-casts votes each round and updates viability thresholds rather than accumulating previous vote totals (Malafeyev et al., 2017). In still another direction, DMVR is iterative and accumulative only in the sense of asynchronous local state aggregation over a fixed initial vote profile rather than repeated public ballot rounds (Salehkaleybar et al., 2017).

This heterogeneity matters because the same label can denote very different state-transition structures. In one usage, MAV means additive vote carryover across public rounds. In another, it means thresholded frequency aggregation over repeated stochastic outputs. Related work broadens the design space further by showing that accumulation can occur through ranked-depth expansion, support transfers, or distributed union/intersection updates rather than through literal addition of ballots.

2. Two-round additive electoral procedures

The clearest institutional MAV construction in the cited literature is the two-round rule proposed in "Repeat Voting" (Hart, 2022). Its mechanism is stated in four parts: voting is carried out in two rounds; every eligible voter is entitled and encouraged to vote in each of the two rounds; all votes of the two rounds are added up and the final election result is obtained by applying the current election rules to these two-round totals; and the results of the first round are officially counted and published before the second round, which takes place after a delay. A faithful formalization given in the source material is

$T = R_1 + R_2,$

or candidatewise,

$T_c = R_{1,c} + R_{2,c}.$

This construction is explicitly general across “plurality, special majority, electoral college, and so on,” and is discussed for referenda, candidate elections, and parliamentary or multi-party settings. Its rationale is primarily informational and behavioral rather than theorem-driven: round 1 becomes a “de facto giant opinion poll,” but one that is “much more truthful” because its votes count toward the final result; observed round-1 outcomes may mobilize otherwise inactive voters in round 2; and the two-round additive structure may average out late shocks, false information, bad weather, or other one-off disturbances. At the same time, the paper explicitly notes possible procrastination, bandwagon effects, and the effective double influence of voters who participate in both rounds.

"Assessment Voting in Large Electorates" gives a more formal two-round accumulative rule, but for binary decisions under costly voting (Gersbach et al., 2017). In Assessment Voting, a randomly selected Assessment Group votes in round 1, the round-1 tally is published, the remaining citizens may vote or abstain in round 2, and “the votes from both rounds are aggregated” under majority rule, with ties broken by fair randomization. The key state variable is the first-round vote difference $d$ , and round-2 turnout is endogenous to that published cumulative margin. The paper proves that for every $\varepsilon>0$ , there exists $N_1^*$ such that when the first-round group is large enough, with probability at least $1-\varepsilon$ : all first-round citizens vote for their preferred alternative, no second-round citizen votes, and the majority-preferred alternative $A$ is chosen. It also states a welfare comparison in which, for sufficiently large electorates, $W^{AV} > \max\{W^{vol},W^{com}\}$ .

These two papers share the essential MAV pattern of publicly observed interim accumulation with a final decision based on the sum across rounds, but they differ sharply in institutional assumptions. Repeat Voting gives every eligible voter the right to vote in both rounds and offers mostly informal arguments about turnout, information, and representativeness. Assessment Voting instead uses a randomly selected and subsidized first-round sample, restricts the formal model to two alternatives, and derives equilibrium results in a Poisson costly-voting framework. The shared lesson is that additive carryover is not a cosmetic detail: it is the mechanism that makes the first round both consequential and informative.

3. Multi-stage committee rules and elimination models

"A Unified Framework of Multi-Stage Multi-Winner Voting" provides the most explicit general theory of staged committee choice, even though it does not define MAV itself (Gong et al., 2024). The framework starts from an election $E=(C,V)$ and defines a $t$ -stage rule $T_c = R_{1,c} + R_{2,c}.$ 0 with decreasing target sizes $T_c = R_{1,c} + R_{2,c}.$ 1. A final committee $T_c = R_{1,c} + R_{2,c}.$ 2 of size $T_c = R_{1,c} + R_{2,c}.$ 3 is produced if there exists a sequence $T_c = R_{1,c} + R_{2,c}.$ 4 with $T_c = R_{1,c} + R_{2,c}.$ 5, $T_c = R_{1,c} + R_{2,c}.$ 6, and

$T_c = R_{1,c} + R_{2,c}.$ 7

The paper is explicit that “the only state passed across rounds is the surviving candidate set” and that there is “no explicit state variable for accumulated scores, budgets, utilities, or vote weights.” In this sense it is a successive-shortlisting or elimination framework, not literal vote accumulation. Its main theoretical message is axiomatic. If each stage rule satisfies Solid Coalition, then the multi-stage rule also satisfies Solid Coalition. By contrast, for rational multi-stage score-based rules, Committee Monotonicity, Candidate Monotonicity, and Consistency do not preserve. For MAV research, this framework is important less as a direct model of accumulation than as a formal warning that stage composition can preserve some representational guarantees while destroying several standard monotonicity and consistency properties.

"Multistage Voting Model with Alternative Elimination" is even farther from literal MAV, but it sharpens the distinction between repeated voting and accumulative voting (Malafeyev et al., 2017). Here the process is a multistage repeated game with elimination by threshold. Each voter $T_c = R_{1,c} + R_{2,c}.$ 8 has a vote endowment $T_c = R_{1,c} + R_{2,c}.$ 9, but in each round all of that weight is assigned to exactly one alternative. At stage $d$ 0, alternative $d$ 1 receives

$d$ 2

and survives iff $d$ 3. The next round reopens voting among survivors, $d$ 4, and the paper’s distinctive device is a threshold update rule that redistributes the “threshold mass” of eliminated alternatives among survivors in proportion to prior surplus $d$ 5. Under the sufficient condition that the total threshold sum exceeds the total number of available votes, at least one alternative is eliminated in every stage and the process terminates in at most $d$ 6 stages.

Taken together, these papers delimit an important conceptual boundary. A procedure can be multi-stage, path dependent, and highly structured while still not being accumulative in the sense of cross-round tally carryover. In one model, what persists is only a restricted candidate set; in the other, it is the combination of survivors and updated thresholds. MAV, if understood strictly, requires more than staging: it requires some form of support carryover or cumulative aggregation.

4. Iterative accumulation beyond standard elections

Several papers develop MAV-adjacent mechanisms in which accumulation occurs through iterative state updates, ranked support expansion, or voter-local transfers rather than through public addition of ballot totals.

"Distributed Voting/Ranking with Optimal Number of States per Node" studies a Distributed Multi-choice Voting/Ranking algorithm in which nodes repeatedly update local set-valued states through union and intersection operations (Salehkaleybar et al., 2017). There are $d$ 7 possible choices, each node starts with one choice or, in an extension, multiple choices, and pairwise asynchronous interactions are driven by Poisson clocks. The core update gives the smaller-cardinality set the union and the larger-cardinality set the intersection; ranking adds memory sets and, in a compact implementation, uses $d$ 8 nodal states, while voting uses $d$ 9 nodal states. The paper proves finite-time correctness with probability one on connected graphs and gives $\varepsilon>0$ 0 time complexity in complete graphs for fixed vote percentages, inversely proportional to the minimum vote-percentage gap. This is not a public multi-round election, but it is an accumulative protocol in which local states compress and propagate the information needed to recover the plurality winner or the full ranking.

"An algorithm for a fairer and better voting system" develops a ranked, non-eliminative cumulative-support rule that is also close to MAV in mechanism, though not in name (Grama, 2021). Ballots are rankings; support for candidate $\varepsilon>0$ 1 after stage $\varepsilon>0$ 2 is

$\varepsilon>0$ 3

and the printed stage score is

$\varepsilon>0$ 4

No candidate is eliminated. Instead, lower-preference support is added stage by stage until some candidate crosses a threshold $\varepsilon>0$ 5, with variants involving a null candidate $\varepsilon>0$ 6, a dissatisfaction threshold $\varepsilon>0$ 7, an upper validity threshold $\varepsilon>0$ 8, and stage selectors such as First, Last, MinEntropy, MaxEntropy, MinVariance, MaxVariance, and MaxStDev. The source material explicitly notes an internal inconsistency between the printed normalization and the worked score table, which behaves more like a top- $\varepsilon>0$ 9 approval interpretation. Even with that caveat, the paper is a clear example of accumulative voting by ranked-depth expansion rather than by elimination or numeric point budgeting.

"Participatory Budgeting with Cumulative Votes" is single-round rather than multi-round, but it contributes a transfer-based logic that is highly relevant to MAV (Skowron et al., 2020). Each voter allocates unit vote mass across projects, and the preferred rule Minimal Transfers over Costs (MTC) combines support-over-cost prioritization, transfer-based rescue of projects that are eligible by transfers, and Acceptance of Undersupported Projects. Its strongest theorem is that MTC satisfies Strong Proportional Representation, while the paper also shows that all studied rules fail Support Monotonicity and that MTC fails Splitting and Merging Monotonicity. For MAV design, the main significance is the rule’s voter-local transfer principle: excess or stranded support should be reallocated within each voter’s expressed support graph rather than discarded globally.

5. MAV as an inference-time aggregation mechanism in LLMs

The most explicit recent technical use of the term MAV appears in "System Report for CCL25-Eval Task 10: SRAG-MAV for Fine-Grained Chinese Hate Speech Recognition" (Wang et al., 24 Jul 2025). In this paper, MAV is the final inference-stage decision module in a pipeline consisting of Task Reformulation (TR), Self-Retrieval-Augmented Generation (SRAG), generation, MAV, and back-conversion from triplet to quadruplet. The voting unit is the generated triplet output. For each input text, SRAG retrieves the top- $N_1^*$ 0 similar training samples, with the main system fixing $N_1^*$ 1; each retrieved example is concatenated with the input to form a distinct prompt; the fine-tuned Qwen2.5-7B model generates triplets from these prompts; and MAV accumulates frequency counts of produced triplets across prompts and across inference rounds until the most frequent triplet exceeds a threshold $N_1^*$ 2, with the main configuration using $N_1^*$ 3. A faithful reconstruction supplied in the source material defines

$N_1^*$ 4

selects

$N_1^*$ 5

and stops when $N_1^*$ 6 or possibly $N_1^*$ 7, since the paper’s wording is inconsistent on strictness. The prompt diversity confirmed by the paper comes from the top- $N_1^*$ 8 retrieved examples; re-retrieval across rounds, decoding details beyond temperature $N_1^*$ 9, tie-breaking, normalization, and a maximum-round policy are not specified.

In this usage, MAV is explicitly an unweighted count accumulation mechanism. The paper states no weighting by retrieval similarity, generation confidence, prompt quality, or round index. Empirically, the ablation table reports the progression Base Model $1-\varepsilon$ 0, $1-\varepsilon$ 1TR $1-\varepsilon$ 2, $1-\varepsilon$ 3TR $1-\varepsilon$ 4 SRAG $1-\varepsilon$ 5, and $1-\varepsilon$ 6TR $1-\varepsilon$ 7 SRAG $1-\varepsilon$ 8 MAV $1-\varepsilon$ 9 for Hard, Soft, and Average Score respectively. The threshold sensitivity analysis over $A$ 0 shows Hard Score rising from $A$ 1 to $A$ 2, Soft Score from $A$ 3 to $A$ 4, and Average Score from $A$ 5 to $A$ 6. The paper’s documented limitation is computational: “MAV’s high voting thresholds increase computational costs.”

This interpretation of MAV differs sharply from electoral usage. The accumulating objects are generated structures, not citizens’ ballots; the rounds are repeated stochastic inference passes rather than temporal voting events; and the stopping rule is threshold-based dominance rather than a fixed election date. Even so, the underlying logic is recognizably accumulative: repeated noisy outputs are treated as evidence streams whose frequencies are aggregated until one candidate answer is stable enough to trust.

6. Design tensions, misconceptions, and open problems

A recurrent misconception in the literature is to equate all staged procedures with accumulative voting. The cited papers show that this is false. Repeat Voting and Assessment Voting are accumulative because earlier-round votes remain in the final outcome, whereas the unified multi-stage multi-winner framework and the alternative-elimination model are staged but non-accumulative in the literal tally-carryover sense (Hart, 2022, Gong et al., 2024). The term MAV therefore requires care: the key question is not whether there are several stages, but what state is preserved and how it enters the final decision rule.

Another recurring tension concerns the informational role of interim publication. In Repeat Voting, publication of the first-round tally is central because it turns round 1 into a consequential public signal that may improve turnout, information aggregation, and representativeness; the same paper also notes bandwagon effects, herding-like dynamics, tactical coordination, demobilization, and the unequal effective influence of citizens who vote in both rounds (Hart, 2022). Assessment Voting formalizes a more disciplined version of the same feedback logic: once the first-round cumulative lead is large enough, the only equilibrium of round 2 is no further turnout (Gersbach et al., 2017). The shared implication is that public interim accumulation is simultaneously an informational device and a strategic intervention.

Fairness and proportionality generate a different set of problems. Transfer-based cumulative rules can correct coordination failures, as in Minimal Transfers over Costs, but this comes with strong path dependence: the participatory-budgeting paper proves that all studied rules fail Support Monotonicity and that MTC fails Splitting and Merging Monotonicity (Skowron et al., 2020). The multi-stage committee framework similarly shows that rational stage composition generally destroys Committee Monotonicity, Candidate Monotonicity, and Consistency (Gong et al., 2024). A plausible implication is that richer inter-round carryover often improves representational or robustness goals only by sacrificing some standard invariance properties.

The open problems stated or implied across the literature are substantial. The repeat-voting paper explicitly leaves unresolved what happens in truly iterative environments with many rounds, whether later rounds should have declining or increasing weights, whether one should cap total votes per voter, how equilibrium turnout and strategic coordination evolve, whether public disclosure after every round is desirable, and how to control bandwagon and herding effects in broader MAV systems (Hart, 2022). The machine-learning use of MAV leaves different engineering questions open: tie-breaking, canonicalization of structured outputs, confidence weighting, re-retrieval policies, and stopping behavior if the threshold is never reached (Wang et al., 24 Jul 2025). Across both social-choice and algorithmic settings, the central unresolved issue is the same: how to exploit iterative accumulation without allowing the accumulation path itself to dominate the quality or fairness of the final outcome.