Veto: Applications in Science and Decision Theory

• Veto is a rule that excludes an event or candidate based on an additional negative condition, as seen in anticoincidence logic, forced-zero Boolean functions, and veto interval graphs.
• In experimental physics and detector systems, veto mechanisms optimize background rejection by balancing dead time and live-time cost to enhance signal fidelity.
• In social choice and graph theory, veto procedures protect minority interests and enforce decisive constraints, shaping voting systems and structural network properties.

Searching arXiv for the cited papers to ground the article and verify metadata. Veto denotes a blocking or exclusion rule that suppresses an event, outcome, candidate, or state when ancillary evidence or structural constraints indicate that it should not survive. In the literature, the term ranges from temporal anticoincidence logic in gravitational-wave searches, to active detector subsystems that tag cosmogenic or hadronic backgrounds, to jet-activity exclusions in collider analyses, to minority-protection and delegation rules in voting and bargaining, and to formal objects such as Boolean veto functions and veto interval graphs (Pal, 6 Jan 2026, Kondratev et al., 2018, Ebadi et al., 2014, Flesch et al., 2017).

1. Core meanings and formal patterns

A recurrent structure of veto rules is that acceptance is not determined solely by the candidate object itself, but by an additional negative condition. In the gravitational-wave anticoincidence setting, a trigger is vetoed when it is unusually loud in one detector and has no corresponding trigger in the other detector within the expected coincidence window. The rule is written in XOR form,

$$\text{Output Y (Veto)}= \begin{cases} 0, & A=0,\; B=0\ 1, & A=1,\; B=0\ 1, & A=0,\; B=1\ 0, & A=1,\; B=1 \end{cases}$$

so that exactly one loud detector state activates the veto, whereas coincident loud states are retained as potentially astrophysical (Pal, 6 Jan 2026).

In Boolean network theory, the same asymmetry appears as a forced-zero logic. A veto function $f_v$ is defined by disjoint activator and inhibitor sets $A$ and $I$, with

$$f_v(\sigma)=1 \Leftrightarrow \left(\forall j\in I:\sigma_j=0\right)\ \text{and}\ \left(\exists l\in A:\sigma_l=1\right).$$

Any single inhibitory input can therefore force the output to $0$, regardless of all activators. This is a stricter form of inhibition than ordinary threshold balancing, and it is representable by weights $w_j\in\{-k,0,+1\}$ and threshold $\theta=0$ (Ebadi et al., 2014).

In graph theory, veto is implemented geometrically. A veto interval $I(a)=(a_l,a_v,a_r)$ is a closed interval with an interior veto mark $a_v$, and two vertices are adjacent only when the corresponding intervals intersect while neither contains the other’s veto mark. Formally, adjacency holds iff

$f_v$0

This marked-interval rule immediately yields the structural fact that veto interval graphs are triangle-free (Flesch et al., 2017).

Across these settings, veto is thus not merely exclusion in an informal sense. It is a negative admissibility criterion: a single-detector trigger lacks network support, an inhibitor dominates activators, or an interval overlap is invalidated by a veto mark. This suggests a common interpretation in which veto rules encode decisive counterevidence rather than weak penalty.

2. Anticoincidence and auxiliary vetoes in gravitational-wave searches

In transient gravitational-wave searches, vetoes are used to suppress terrestrial noise without discarding plausible astrophysical events. The anticoincidence veto for binary-black-hole matched filtering exploits the fact that genuine transients should be observed coincident in time at geographically separated observatories, whereas local glitches are generally non-coincident. For the LIGO Hanford–Livingston pair, the coincidence window is about $f_v$1, consistent with the intersite light-travel time. The implementation described for the HL network divides coincident data into overlapping stretches of about $f_v$2, runs a particle swarm optimization search over BBH parameters using IMRPhenomXAS templates, forms triggers at SNR above about $f_v$3, reweights them with the power $f_v$4-veto and the sine-Gaussian veto, discards triggers with reweighted-SNR/SNR ratios below unity, often below about $f_v$5, and then applies anticoincidence to triggers louder than about $f_v$6 in reweighted SNR. Background estimation uses time slides typically around $f_v$7, and vetoed intervals are removed self-consistently from the observed time so that the false-alarm-rate estimation is not biased. In a 30-day O3a demonstration with about $f_v$8 days of coincident time, the veto removed roughly $f_v$9 minutes of coincident data, brought the background closer to the Gaussian limit, and increased the number of recovered injections at essentially all IFAR thresholds, with the gain strongest for moderate-SNR and expected to be especially useful for short-duration transient signals (Pal, 6 Jan 2026).

A different gravitational-wave use of vetoes relies on auxiliary channels rather than detector-network timing. The Ordered Veto List algorithm constructs veto configurations from an auxiliary channel name, a threshold on auxiliary glitch significance, and a time window around each selected auxiliary glitch. It evaluates each configuration by efficiency,

$A$0

fractional dead-time,

$A$1

and the ratio $A$2, together with a Poisson significance for the observed number of coincidences. Configurations are ordered by $A$3 and applied hierarchically so that removed glitches and dead-time are excluded from later steps. In the reported LIGO studies, time windows $A$4 and Kleine-Welle significance thresholds $A$5 were used. Earlier applications rejected $A$6–$A$7 of single-detector glitches and $A$8–$A$9 of coincident background with under $I$0 dead-time, and the later S4 and S6 studies showed that most performance was achieved after about two iterations while the ordered configuration list compressed strongly by iteration $I$1 (Essick et al., 2013).

For continuous-wave searches, the veto problem is not transient coincidence but astrophysical phase consistency. The DM-off veto compares the significance of a standard Doppler-modulated search against a search in which the Doppler modulation is turned off while amplitude modulation is retained. The veto is tuned on $I$2 fake-signal injections so that none are rejected, giving a false dismissal rate less than $I$3 in $I$4, i.e. $I$5. The threshold is

$I$6

and a candidate is rejected if the DM-off statistic exceeds that threshold. Applied to the $I$7 candidates from the Einstein@Home O1 low-frequency all-sky search, the veto classified $I$8 as coherent disturbances, i.e. $I$9, leaving four survivors after the full three-step hierarchy (Zhu et al., 2017).

These gravitational-wave implementations differ in mechanism but share a network-consistency principle. Anticoincidence vetoes reject loud isolated triggers, OVL rejects intervals of livetime supported by auxiliary-channel correlations, and DM-off rejects candidates that are better explained by terrestrial coherence than by astrophysical Doppler structure.

3. Active veto detectors in rare-event and intensity-frontier experiments

In detector physics, veto commonly denotes an active subsystem that tags backgrounds which would otherwise mimic the target process. The underlying logic is anticoincidence rather than statistical down-ranking: if the shielding, scintillator, or auxiliary calorimeter sees a signature characteristic of a background process, the primary event is rejected.

For cosmogenic-spallation rejection in large liquid scintillator, the veto problem is dominated by $$f_v(\sigma)=1 \Leftrightarrow \left(\forall j\in I:\sigma_j=0\right)\ \text{and}\ \left(\exists l\in A:\sigma_l=1\right).$$0Li and $$f_v(\sigma)=1 \Leftrightarrow \left(\forall j\in I:\sigma_j=0\right)\ \text{and}\ \left(\exists l\in A:\sigma_l=1\right).$$1He backgrounds that can mimic inverse beta decay. In a $$f_v(\sigma)=1 \Leftrightarrow \left(\forall j\in I:\sigma_j=0\right)\ \text{and}\ \left(\exists l\in A:\sigma_l=1\right).$$2 kton detector such as JUNO, with total muon rate $$f_v(\sigma)=1 \Leftrightarrow \left(\forall j\in I:\sigma_j=0\right)\ \text{and}\ \left(\exists l\in A:\sigma_l=1\right).$$3 Hz, KamLAND-style aggressive vetoes are too costly. The optimized strategy is a two-component veto: a cylindrical veto for tracked muons and a full-detector veto for poorly tracked showering muons. With perfect tracking, the optimal hierarchy configuration uses $$f_v(\sigma)=1 \Leftrightarrow \left(\forall j\in I:\sigma_j=0\right)\ \text{and}\ \left(\exists l\in A:\sigma_l=1\right).$$4 GeV, $$f_v(\sigma)=1 \Leftrightarrow \left(\forall j\in I:\sigma_j=0\right)\ \text{and}\ \left(\exists l\in A:\sigma_l=1\right).$$5 s, and $$f_v(\sigma)=1 \Leftrightarrow \left(\forall j\in I:\sigma_j=0\right)\ \text{and}\ \left(\exists l\in A:\sigma_l=1\right).$$6 m, giving $$f_v(\sigma)=1 \Leftrightarrow \left(\forall j\in I:\sigma_j=0\right)\ \text{and}\ \left(\exists l\in A:\sigma_l=1\right).$$7 cylindrical veto efficiency and $$f_v(\sigma)=1 \Leftrightarrow \left(\forall j\in I:\sigma_j=0\right)\ \text{and}\ \left(\exists l\in A:\sigma_l=1\right).$$8 live time, while $$f_v(\sigma)=1 \Leftrightarrow \left(\forall j\in I:\sigma_j=0\right)\ \text{and}\ \left(\exists l\in A:\sigma_l=1\right).$$9 falls from $0$0 to $0$1. For $0$2, the optimal cylindrical veto efficiency is $0$3, with $0$4 GeV, $0$5 s, $0$6 m, $0$7 live time, and $0$8 compared with $0$9 with no background. The paper’s central point is that the optimal veto is surprisingly loose, because additional rejection rapidly costs live time while the unrejected background can still be constrained and subtracted (Grassi et al., 2015).

Several experiments implement hardware vetoes as dedicated detector upgrades. In NA64, a prototype veto hadron calorimeter built from $w_j\in\{-k,0,+1\}$0 layers of $w_j\in\{-k,0,+1\}$1 mm copper interleaved with $w_j\in\{-k,0,+1\}$2 layers of $w_j\in\{-k,0,+1\}$3 mm scintillator was installed downstream to intercept large-angle hadrons and photon-nuclear secondaries escaping the main acceptance. With $w_j\in\{-k,0,+1\}$4 electrons on target, it rejected the upstream-electroproduction background by more than an order of magnitude and enabled the missing-energy threshold to be reduced from $w_j\in\{-k,0,+1\}$5 GeV to $w_j\in\{-k,0,+1\}$6 GeV, with a detailed data-driven background estimate of

$w_j\in\{-k,0,+1\}$7

for $w_j\in\{-k,0,+1\}$8 EOT (Andreev et al., 14 Mar 2025). In the CROSS $w_j\in\{-k,0,+1\}$9 program, a nine-sector muon veto surrounding the cryogenic setup uses either $\theta=0$0 or $\theta=0$1 trigger logic; combined with the multiplicity cut of thermal detectors, the two-sector and single-sector logics reject $\theta=0$2 and $\theta=0$3 of muon-induced events in the ROI, respectively. The adopted single-sector strategy incurs dead time of about $\theta=0$4 but reduces the ROI background to $\theta=0$5 (Barabash et al., 31 Oct 2025). In the GeSparK HPGe+LS coincidence detector, an upgraded six-panel plastic-scintillator veto with four panels placed between the copper and lead layers achieved a measured $\theta=0$6 background reduction over $\theta=0$7–$\theta=0$8 keV and $\theta=0$9 reduction for saturated HPGe events above $I(a)=(a_l,a_v,a_r)$0 keV, compared with a Monte Carlo expectation of $I(a)=(a_l,a_v,a_r)$1 veto efficiency (Barresi et al., 17 Feb 2025). At miniICAL, the CMVD based on extruded plastic scintillators, wavelength-shifting fibers, and SiPMs is designed for efficiency better than $I(a)=(a_l,a_v,a_r)$2 with false-positive rate below $I(a)=(a_l,a_v,a_r)$3; simulation with a $I(a)=(a_l,a_v,a_r)$4 p.e. threshold, at least two SiPMs above threshold per strip, and a $I(a)=(a_l,a_v,a_r)$5 cm matching window supports the required $I(a)=(a_l,a_v,a_r)$6 veto efficiency with negligible fake rate (Shah et al., 2024).

Dark-matter searches provide a more elaborate use of veto subsystems because the backgrounds of concern are neutron-like and hence WIMP-like in the primary detector. The ZEPLIN-III anti-coincidence detector combined $I(a)=(a_l,a_v,a_r)$7 plastic scintillator bars with gadolinium-loaded polypropylene to tag neutron captures. Design studies predicted rejection of over $I(a)=(a_l,a_v,a_r)$8 of neutron events satisfying WIMP selection, a reduction of the background in the WIMP region from $I(a)=(a_l,a_v,a_r)$9 to $a_v$0 events yr$a_v$1, and gamma tagging above $a_v$2 (Akimov et al., 2010). Operational data then measured near-unity live time relative to ZEPLIN-III, prompt gamma tagging of $a_v$3, total neutron tagging of $a_v$4, prompt and delayed accidental rates of $a_v$5 and $a_v$6, and an inferred residual neutron background of $a_v$7 events per year in the WIMP acceptance region (Ghag et al., 2011). A conceptual boron-loaded liquid-scintillator neutron veto pushed the same logic further: a $a_v$8 m thick veto based on $a_v$9 w/w tri-methyl borate in pseudocumene shortened the neutron capture time from about $f_v$00 in pure pseudocumene to $f_v$01, yielded internal radiogenic-neutron veto efficiency of $f_v$02, maintained better than $f_v$03 efficiency with a $f_v$04 window after inner-detector capture and feed-through effects, and reduced cosmogenic-neutron recoil events by about a factor of $f_v$05 for a $f_v$06 m veto (Wright et al., 2010).

These implementations make clear that detector vetoes are not merely ancillary hardware. They are exposure-defining systems whose optimization is governed by the same trade-off that appears in software vetoes: rejection efficiency versus dead time, acceptance loss, or live-time cost.

4. Jet vetoes in collider phenomenology and measurements

In collider physics, a veto suppresses events with additional hadronic activity beyond a prescribed scale. The operational object is usually a jet veto survival probability or gap fraction, and the theoretical challenge is that the veto introduces logarithmic sensitivity to soft and collinear radiation.

For dileptonic $f_v$07 production at $f_v$08 TeV, the ATLAS measurement defined the gap fraction

$f_v$09

where $f_v$10 counts selected events containing no additional jet above threshold $f_v$11 in the veto region. Additional jets were reconstructed with anti-$f_v$12, $f_v$13, required to satisfy $f_v$14 and $f_v$15, and were studied in the rapidity intervals $f_v$16, $f_v$17, $f_v$18, and $f_v$19. An alternate observable vetoed on the scalar transverse momentum sum of the additional jets. After multiplicative detector corrections $f_v$20, typically about $f_v$21–$f_v$22 at $f_v$23 GeV, the data were compared with MC@NLO, POWHEG, ALPGEN, and SHERPA. The full interval $f_v$24 was described reasonably overall, but in the most central interval $f_v$25 POWHEG predicted a gap fraction that was too large, while in the most forward interval $f_v$26 none of the generators agreed over the full threshold range (Collaboration, 2012).

For dijet production, ATLAS measured the fraction of events surviving a veto on any additional jet with $f_v$27 GeV in the rapidity interval bounded by the two boundary jets. Jets were reconstructed with anti-$f_v$28, $f_v$29, required to satisfy $f_v$30 GeV and $f_v$31, and the measurements were presented as functions of $f_v$32 up to about $f_v$33 units and $f_v$34 GeV. The gap fraction decreased with increasing $f_v$35 and generally with increasing $f_v$36, while the mean number of jets in the gap increased with both variables. Among the generators studied, POWHEG plus parton shower gave the best overall description in many regions, HEJ described the large-$f_v$37, low-$f_v$38 regime well, and ALPGEN showed the largest discrepancies (Collaboration, 2011).

The theoretical status of jet vetoes depends strongly on the observable definition. Inclusive vetoes such as

$f_v$39

are global and can, in principle, be resummed to higher orders. Jet-based exclusive vetoes,

$f_v$40

depend on the jet algorithm and on the jet radius $f_v$41. For $f_v$42, soft-collinear mixing generates $f_v$43 terms starting at NNLL, such as $f_v$44, that are not reproduced automatically by standard soft-collinear factorization. For $f_v$45, clustering induces $f_v$46 terms, with structures of the form

$f_v$47

which contribute at NLL in the exponent and cannot be resummed with the currently available methods. The two-loop coefficients $f_v$48 and $f_v$49 were computed explicitly, and for the $f_v$50 and $f_v$51 values relevant to ATLAS and CMS Higgs analyses the clustering logarithms are numerically important (Tackmann et al., 2012).

In collider usage, therefore, veto is simultaneously an analysis cut and a precision-theory object. It defines exclusive categories experimentally, but also reorganizes perturbation theory by converting unrestricted QCD radiation into logarithmically sensitive no-emission probabilities.

5. Veto power, voting rules, and delegation mechanisms

In social-choice theory, veto power is the dual of majority power. For quota $f_v$52 and number $f_v$53 of least-preferred candidates, a rule satisfies the $f_v$54-veto criterion iff it satisfies the $f_v$55-majority criterion for each $f_v$56. Veto power is measured by the minimal share of voters needed to guarantee that each of their $f_v$57 least-preferred candidates loses. The paper gives exact worst-case quotas for major rules: instant-runoff voting has threshold $f_v$58 for $f_v$59 and in fact for all $f_v$60; plurality has $f_v$61 for all $f_v$62; plurality with runoff has $f_v$63 for $f_v$64 but $f_v$65 for $f_v$66; Borda has $f_v$67 for $f_v$68, $f_v$69 for $f_v$70, $f_v$71 for $f_v$72, $f_v$73 for $f_v$74, and $f_v$75 in the unrestricted table; Black’s rule and proportional veto core are identified as minority-protective exceptions with relatively low majority power but high veto power (Kondratev et al., 2018).

A different voting-theoretic meaning of veto appears in metric distortion. PluralityVeto initializes each candidate with plurality score

$f_v$76

then runs an $f_v$77-round process in which voter $f_v$78 vetoes her bottom choice among the candidates whose current score is still positive,

$f_v$79

and decrements that score by one until the last standing candidate wins. The rule uses only two queries per voter, a top query and a bottom-among query, yet achieves distortion $f_v$80, which is the optimal deterministic metric-distortion bound. Its randomized $f_v$81-round extension, RoundPluralityVeto$f_v$82, chooses the winner with probability proportional to residual score after $f_v$83 veto rounds and also has distortion at most $f_v$84 for all $f_v$85 (Kizilkaya et al., 2022).

In economic mechanism design, veto denotes the principal’s power to retain the status quo rather than randomizing among non-status quo alternatives. When the principal is more risk-averse than the agent toward non-status quo options and the agent has state-independent preferences, an optimal direct mechanism is only if it is a veto mechanism: $f_v$86 The principal randomizes only between the status quo $f_v$87 and a single non-status quo action. In the one-dimensional quadratic formulation, the key function is

$f_v$88

and in the valuable-veto case the optimal mechanism pools below a threshold $f_v$89 and uses veto only when the state exceeds that threshold, with

$f_v$90

The status quo functions as a punishment device that keeps the agent indifferent across reports (Hu et al., 2022).

Veto bargaining studies a related but distinct environment in which a proposer offers a delegation set to a veto player who can accept an action or veto to the status quo $f_v$91. Full delegation is the interval $f_v$92, no compromise is the singleton offer of the proposer’s ideal action $f_v$93, and the intermediate mechanism is interval delegation $f_v$94. Under logconcavity of the type density in the linear-quadratic class, interval delegation is optimal, and full delegation is optimal if $f_v$95 is decreasing on $f_v$96. The expected payoff of interval delegation is

$f_v$97

with first-order condition

$f_v$98

Here veto is not merely a blocking right; it is the status-quo fallback around which the whole optimal menu is organized (Kartik et al., 2020).

Taken together, these results show that veto in collective choice has two analytically distinct forms. One is a protection against disliked outcomes, quantified by minimal coalition thresholds. The other is a procedural device that disciplines proposals or candidates through the ever-present possibility of exclusion.

6. Veto structures in Boolean dynamics and graph theory

In Boolean dynamics, veto functions form a specific class of update rules intended to capture absolute inhibition in regulatory and signaling systems. For a $f_v$99-ary veto function with $A$00 inhibitors and $A$01 activators, the activity of an inhibitor is

$A$02

the activity of an activator is

$A$03

and the total sensitivity is

$A$04

Within the annealed approximation, $A$05, $A$06, and $A$07 correspond to ordered, critical, and chaotic dynamics. The ensemble-averaged sensitivity for random inhibitor probability $A$08 has a closed form, and the paper emphasizes that the ensemble average never exceeds $A$09, so random veto-function networks are typically ordered. Empirically, veto functions are at least as over-represented as threshold functions and more over-represented than canalyzing functions in the Helikar et al. intracellular signaling network for arities $A$10, and yeast cell-cycle dynamics can be formulated with none or minimal changes to the wiring diagrams (Ebadi et al., 2014).

In graph theory, veto interval graphs reinterpret the marked-point logic geometrically. Besides the basic adjacency rule, the theory establishes that any VI representation can be perturbed so that all veto marks are distinct, that $A$11 implies $A$12, and that complete bipartite graphs $A$13, cycles $A$14 for $A$15, and trees are VI graphs. The family also has nontrivial exclusions: $A$16 is not a VI graph, and the Grötzsch graph is a minimal forbidden induced subgraph. For subclasses, the paper proves

$A$17

It also shows that UVI graphs are $A$18-colorable, that the chromatic number of a VI graph can be at least $A$19 via $A$20, and that the exact maximum chromatic number of general VI graphs remains open (Flesch et al., 2017).

These abstract theories make explicit something that the experimental uses of veto often leave implicit: veto is a structural asymmetry. In Boolean networks, inhibition is lexicographically stronger than activation. In veto interval graphs, overlap is subordinate to marked-point exclusion. A plausible implication is that veto-based formalisms are especially useful when a system is organized around decisive negative constraints rather than smooth trade-offs.

7. Common trade-offs and recurring limitations

Across the literature, veto design is governed by a repeated optimization problem: maximize rejection of undesirable outcomes while minimizing collateral loss of useful ones. In gravitational-wave transient searches, the anticoincidence veto removes only a small amount of coincident time yet substantially suppresses the non-Gaussian background tail, while OVL explicitly ranks vetoes by efficiency over dead-time and uses Poisson significance to guard against over-training (Pal, 6 Jan 2026, Essick et al., 2013). In large liquid scintillator neutrino detectors, the optimal veto is not the most aggressive one because dead time quickly degrades hierarchy sensitivity and only slightly affects $A$21, whose uncertainty is dominated by reactor-spectrum systematics (Grassi et al., 2015). In CROSS, the adopted $A$22 logic attains stronger rejection but at the cost of $A$23 dead time (Barabash et al., 31 Oct 2025). In ZEPLIN-III and boron-loaded scintillator proposals, capture-enhanced vetoes are optimized to reject neutron-like backgrounds without introducing additional radioactivity or unmanageable accidentals (Ghag et al., 2011, Wright et al., 2010).

Collider jet vetoes exhibit an analogous theoretical trade-off. Large $A$24 mitigates $A$25 clustering logarithms but makes soft-collinear mixing a leading-power issue beyond NLL; small $A$26 restores factorization at leading power but introduces clustering logarithms that are not presently resumable with available methods (Tackmann et al., 2012). In voting and delegation, stronger veto protection for minorities or veto players can also weaken the power of majorities or proposers, with the literature identifying both high-veto-power rules such as IRV and minority-protective exceptions such as Borda and Black’s rule (Kondratev et al., 2018).

The most persistent misconception is that veto is synonymous with maximal rejection. The experimental and formal results do not support that view. The optimal veto can be loose, localized, delayed, probabilistic, or thresholded, and in several domains its value lies as much in background characterization and credible inference as in brute-force exclusion.