Rules Before Oracles: Auditable, User-Configurable Argument Selection for Deliberative Polling

Muntaser Syed; Markus Zanker; Marius Silaghi

cs.AIAug 25, 2026

Rules Before Oracles: Auditable, User-Configurable Argument Selection for Deliberative Polling

Authors: Muntaser Syed, Markus Zanker, Marius Silaghi

Organizations: Florida Institute of Technology, Melbourne, Florida, USA · Free University of Bozen-Bolzano, Bolsano, Italy

Abstract

In a deliberative poll, once submissions outnumber what anyone will read, some mechanism chooses which arguments each voter sees, acquiring much of the decision; practice delegates it to opaque learned rankers, so a voter cannot recompute or contest the exposure that shaped their vote. We ask whether it can be a published rule over publicly recomputable evidence with parameters held by the voter, treating legibility as an admissibility condition on usable mechanisms, not an objective traded against accuracy. We formalise a poll over bipolar justification sets, judging a slate by reason coverage, the order it arrives in, and captured endorsement mass; we give seven checkable criteria for a civic recommender and a rule meeting them: a one-hop reversed endorsement flow parameterised by a relation-weight function. An agentic simulator records every slate at every vote, over about 17,000 seed-paired runs. Served slates fall 0.035 short of a label-reading ceiling upper-bounding every selection procedure, opaque ones included: any unconstrained ranker's advantage is bounded and small. On coverage alone, with non-degenerate authoring, the rule is indistinguishable from a random slate, a null due to an order-blind, charity-blind instrument; on the other two it leads at every prefix by a margin widening with adversarial pressure and dominates on mass by a factor of 3.3. Once a realistic fraction of submissions carries no reasons, the coverage margin returns and grows. Label-homogeneous flooding collapses completeness from 0.81 to 0.34 under a flat weight policy, only to 0.44 under author-count normalisation, making the weight function a security control worth 10% of completeness. The choice between ranking arms is a position on a coverage-versus-mass frontier, not a fact, the kind of choice only a legible rule can hand to the person it affects. It maps onto an open-source peer-to-peer platform.

Figures & tables

Panel of Figure 1 — Figure 1. The two pipelines. Both consume the same corpus and both emit $K$ items. The upper one additionally consumes behavioural telemetry and passes it through parameters nobody outside can inspect, so a disputed slate has no derivation to point at. The lower one consumes only evidence every participant can already retrieve — who endorsed what, and which signed links exist — and exposes its policy parameters to the individual voter, so a disputed slate reduces either to a disputed input, which is checkable, or to a disputed policy, which is arguable. This manuscript treats the difference as a condition of admissibility rather than as a term in an objective.

	endorsement rule	greedy cover	learned ranker
	(§ 4.4 )	(§ 3.5 )
C 1 determinism	yes	yes	only if frozen
C 2 evidence locality	one hop	whole pool –	unbounded –
C 3 author blindness	yes	tie-breaks	learned from behaviour –
C 4 semantic abstinence	yes	reads labels –	reads everything –
C 5 reproducibility	yes	yes	needs exact checkpoint –

Table 1. The seven criteria against three mechanism families. – denotes failure by construction rather than by implementation choice: no amount of engineering effort within that family recovers the property. The greedy cover is included because it appears throughout the evaluation and it is important to be explicit that it is inadmissible; see Principle 1 .

policy	$\omega_{\mathrm{r}}(j,k)$	reads	under flood
flat	$1$	nothing beyond the link’s existence	$0.34$
author-normalised	$\|A(j,k)\|\,/\,\max(1,V^{\sigma(k)})$	how many distinct people asserted it, against how many voted on that side	$0.44$

Table 2. The two relation-weight policies. The last column previews Section 9.2 : mean combined completeness under a flooding coalition holding a quarter of the electorate , at the reference configuration.

Quantity	Mean	Std
Combined completeness, mean over constituents	0.806	0.038
Combined completeness, median over constituents	0.886	0.042
Within-run spread of completeness	0.213	0.032
Live endorsing vocabulary (of $30$ )	30.0	0.0
Live opposing vocabulary (of $30$ )	29.9	0.3
Authored endorsing justifications	48.3	6.6

Table 3. The reference configuration characterised: BRA proposition,

\pi_{\mathrm{own}}=0.10

K=20

\pi_{\mathrm{lnk}}=0.60

N=1000

, author-normalised

\omega_{\mathrm{r}}

; mean

\pm

standard deviation over ten seeds. Completeness is that of the slate the endorsement rule actually served. “Within-run spread” is the standard deviation of per-constituent completeness inside a single run, averaged over seeds: it measures temporal inequity, not experimental noise, and at

0.213

it is more than five times the across-seed variation.

Figure 2. Vocabulary saturation under three authoring rates, anchored at the measured saturation points (

\approx 800

constituents at

\pi_{\mathrm{own}}=0.02

\approx 150

\pi_{\mathrm{own}}=0.30

, in runs of

N=1000

); the vertical rules mark the measured anchors and the shape between them is illustrative. The area to the left of each curve is the population that voted against a reason space still under construction — the quantity a deployment reduces by raising the authoring rate, not by ranking better.

Lever (settings)	prop.	$\bar{c}$ by setting
$\pi_{\mathrm{own}}\in\{0.02,0.05,\mathbf{0.10},0.20,0.30\}$	BRA	0.702	0.713	0.806	0.841	0.878
	UBI	0.684	0.751	0.804	0.853	0.873
$K\in\{5,10,15,\mathbf{20},30\}$	BRA	0.448	0.666	0.763	0.806	0.833
$K\in\{5,10,15,\mathbf{20},30\}$	UBI	0.448	0.666	0.768	0.804	0.832
$\pi_{\mathrm{lnk}}\in\{0.20,0.40,\mathbf{0.60},0.80,1.00\}$	BRA	0.806	0.804	0.806	0.804	0.804
	UBI	0.799	0.801	0.804	0.805	0.802

Table 4. Mean combined completeness

\bar{c}

at every setting of every lever, both propositions, author-normalised weight policy, ten seeds per cell. Settings run left to right in the order given in the row label; the reference setting is in bold. Across-seed

\sigma

runs

0.013

–

0.082

throughout and is tabulated per cell in the online appendix. In the authoring-rate row

\pi_{\mathrm{reuse}}=0.50

is fixed and

\pi_{\mathrm{abst}}

absorbs the remainder; all other levers are held at reference.

	End-of-round vocabulary			Live vocabulary
	Served	Ceiling	Gap	Served	Ceiling	Gap
Mean over seeds	0.806	0.837	0.031	0.968	1.000	0.032
Std over seeds	0.038	0.034	0.014	0.015	0.000	0.015
Minimum	0.750	0.793	0.011	0.940	1.000	0.011
Maximum	0.862	0.888	0.059	0.989	1.000	0.060

Table 5. Served completeness against the label-reading greedy ceiling, reference configuration (BRA), summarised over ten seeds; the per-seed rows are in the online appendix. The ceiling is evaluated on the same pool and at the same cache refresh as the served slate, so the gap isolates selection quality rather than index staleness. The left block scores against the end-of-round vocabulary, the right block against the vocabulary live at the moment of serving (Definition 3.4 ). The ceiling saturates the live vocabulary in every seed, so the two gaps almost coincide and the residual shortfall in the left block is temporal rather than algorithmic.

$K$	full	endorse-only	enhance-only	attack-only	random
$5$	0.4500	0.4470	0.4509	0.4498	0.4475
$10$	0.6706	0.6708	0.6712	0.6723	0.6652
$20$	0.8205	0.8199	0.8202	0.8213	0.8181
$30$	0.8511	0.8505	0.8510	0.8510	0.8506

Table 6. Ranking-term ablation in an non-degenerate authoring attack-free electorate: mean combined completeness pooled over the two propositions,

100

seed-paired seeds per cell. The live pool holds about

51

items per side throughout, so

K

is also a proxy for the fraction of the pool served. Across-seed

\sigma

runs

0.026

–

0.049

for the four ranked arms and

0.015

–

0.025

for the random arm.

Figure 3. Prefix coverage against slate depth at

K=20

, pooled over both propositions,

2800

stored runs. Panels: attack-free electorate, coalition at a tenth, coalition at a quarter. The shaded region is what the endorsement rule delivers above the uniform draw at each depth; ticks on the axis mark

e_{90}

, the depth at which each arm reaches nine tenths of its own final coverage. The three arms meet at

m=20

in the attack-free panel and separate everywhere before it, by a margin that widens with attack; under attack the endorsement rule ends

m=20

below the draw — the only quantity Table 6 could see — and leads it at every earlier depth.

$\|A\|$	arm	$p_{1}$	$p_{3}$	$p_{5}$	$p_{10}$	$\mathrm{AUC}$	$\mathrm{RDC}$	$e_{90}$	$p_{20}$
$0$	full	0.1290	0.3301	0.4738	0.6865	0.4466	1.3298	11.74	0.8205
	endorse-only	0.1281	0.3267	0.4720	0.6872	0.4451	1.3258	11.68	0.8199
	random	0.1165	0.3054	0.4476	0.6650	0.4284	1.2833	12.28	0.8181
$100$	full	0.1205	0.2919	0.4066	0.5457	0.3648	1.0705	0 9.79	0.6088
	endorse-only	0.1182	0.2898	0.4068	0.5635	0.3732	1.1021	10.49	0.6474
	random	0.0901	0.2048	0.2894	0.4509	0.3060	0.9544	14.38	0.6472

Table 7. Ordering measures at

K=20

, pooled over both propositions, seed-paired,

2800

stored runs.

p_{m}

is prefix coverage at depth

m

;

\mathrm{AUC}

is the mean over depths;

\mathrm{RDC}

is rank-discounted coverage ( 6 );

e_{90}

is the depth reaching nine tenths of that slate’s own final coverage (lower is better).

|A|

is the coalition size out of

N=1000

. Note that

p_{20}

— the only column completeness can see — agrees across arms to within

0.005

in the attack-free electorate, and under attack moves against the ranked rule while every earlier column moves for it.

$G$	$E$	full	endorse-only	random	full $-$ random	$p$	full $-$ endorse
$0.0$	—	0.8232	0.8233	0.8199	$+0.0033$	$0.018$	$-0.0000$
$0.1$	$0.1$	0.7996	0.7982	0.7940	$+0.0056$	$2.3\times 10^{-3}$	$+0.0014$
$0.1$	$0.4$	0.7993	0.7982	0.7940	$+0.0053$	$5.5\times 10^{-3}$	$+0.0011$
$0.3$	$0.1$	0.7479	0.7323	0.7268	$+0.0210$	$3.6\times 10^{-12}$	$+0.0156$
$0.3$	$0.4$	0.7424	0.7323	0.7268	$+0.0156$	$9.2\times 10^{-9}$	$+0.0102$
$0.5$	$0.1$	0.6639	0.6242	0.6248	$+0.0392$	$4.9\times 10^{-15}$	$+0.0397$

Table 8. Degenerate authoring: mean combined completeness against the genuine reason vocabulary, pooled over both propositions,

100

runs per cell, seed-paired across arms.

G

is the fraction of own-authored items that fail to justify;

E

is the share of those that are erroneous supports rather than reason-free.

p

-values are two-sided Wilcoxon signed-rank tests on the full-minus-random contrast. The

G=0

row reproduces the attack-free sweep of Table 6 and serves as the control.

	coverage			endorsement mass			ceiling
regime	full	end.-only	random	full	end.-only	random	mass
$G=0$ , no coalition	0.8232	0.8233	0.8199	0.7560	0.7601	0.4906	0.7905
$G=0.3$	0.7479	0.7323	0.7268	0.7458	0.7610	0.4915	0.7645
$G=0.7$	0.5764	0.5147	0.5104	0.7215	0.7590	0.4906	0.7920
$\|A\|=100$	0.6088	0.6474	0.6472	0.6895	0.6943	0.2916	0.5875
$\|A\|=250$	0.3731	0.4389	0.4437	0.5460	0.5579	0.1673	0.3809

Table 9. Coverage against endorsement mass ( 7 ) across five regimes, pooled over both propositions.

G

is the degenerate fraction at

E=0.1

;

|A|

is coalition size out of

N=1000

. The greedy ceiling attains coverage

1.0000

in every regime, so only its mass is shown. The uniform draw is level with the rule on coverage in the attack-free regime and ahead of it under attack, and loses on mass everywhere, by a factor rising to

3.3

; the ceiling dominates on mass in the three attack-free regimes and is dominated in both attacked ones.

Coalition	normalised	flat	normalised	flat	margin
	BRA		UBI
$0\%$	0.816	0.814	0.815	0.814	—
$5\%$	0.713	0.597	0.708	0.590	$0.117$
$10\%$	0.608	0.440	0.602	0.427	$0.172$
$15\%$	0.519	0.340	0.514	0.331	$0.181$
$20\%$	0.443	0.282	0.430	0.265	$0.163$

Table 10. Flooding attack under spread timing: mean combined completeness against coalition size, both weight policies, both propositions,

200

seeds per cell. The final column gives the defence margin — how much completeness author normalisation retains that a flat policy loses — averaged over the two propositions. Hub-riding, not shown, produces no significant change at any coalition size.

	author-normalised			flat
Coalition	min	gap	$<\!0.5$	min	gap	$<\!0.5$
$0\%$	0.779	0.085	0.118	0.777	0.086	0.118
$5\%$	0.661	0.107	0.130	0.528	0.138	0.348
$10\%$	0.538	0.140	0.257	0.351	0.168	0.782
$15\%$	0.447	0.144	0.581	0.259	0.155	0.941
$20\%$	0.359	0.158	0.878	0.194	0.160	0.987

Table 11. Side imbalance under label flooding, on the runs of Table 10 (200 seeds per cell, pooled over the two propositions). “min” is

\bar{c}^{\min}

of ( 4 ), “gap” the mean over voters of the difference between their two sides, and “

<\!0.5

” the share of voters whose worse side falls below one half.

		no coalition		$10\%$ coalition
Load	arm	$M=1$	$M=200$	$M=1$	$M=200$
$G=0$	full	0.815	0.815	0.707	0.720
	endorse-only	0.815	0.815	0.717	0.729
	random	0.816	0.816	0.742	0.742
	full $-$ random	$-0.0011$	$-0.0015$	$-0.0348^{***}$	$-0.0216^{***}$
$G=0.5$ , $E=0.4$	full	0.642	0.640	0.534	0.539

Table 12. Completeness at the four corners of the refresh-interval

\times

coalition results table, OPT-OUT,

50

seeds per cell, author-normalised weights, co-signed flood at

C=5

M

is the number of constituents between cache refreshes;

M=1

is the reference configuration. The full

-

random rows are seed-paired differences with two-sided paired

t

-tests.

E

is inert at

G=0

Load	arm	$\Delta$	$p$	$\Delta$	$p$
		no coalition		$10\%$ coalition
$G=0$	full	$-0.0004$	$0.79$	$+0.0132$	$3\times 10^{-4}$
	endorse-only	$\phantom{+}0.0000$	exact	$+0.0120$	$5\times 10^{-10}$
	random	$\phantom{+}0.0000$	exact	$\phantom{+}0.0000$	exact
$G=0.5$ , $E=0.4$	full	$-0.0020$	$0.36$	$+0.0050$	$0.17$
	endorse-only	$\phantom{+}0.0000$	exact	$+0.0110$	$4\times 10^{-5}$

Table 13. Cost of lagging the refresh interval, per arm: mean seed-paired

M=200

minus

M=1

completeness, OPT-OUT,

50

seeds. exact marks cells in which the two intervals produce the same completeness on every seed to the last stored digit, so no test applies.

	mean completeness			decomposition
Coalition	heterog.	flooding	(baseline)	$\Delta_{\mathrm{vol}}$	$\Delta_{\mathrm{hom}}$	homog. share
author-normalised weights
$5\%$	0.797	0.711	0.821	$0.024$	$0.086$	$79\%$
$10\%$	0.780	0.609	0.821	$0.040$	$0.172$	$81\%$
$15\%$	0.772	0.519	0.821	$0.049$	$0.253$	$84\%$
$20\%$	0.762	0.435	0.821	$0.058$	$0.328$	$85\%$

Table 14. Decomposing the flooding collapse, pooled over the two propositions,

100

seeds per cell. Heterogeneous is the rate- and corpus-matched control in which attackers author and link at the same inflated rates and aim at the same hubs but draw labels independently.

\Delta_{\mathrm{vol}}

is completeness lost to sheer volume (baseline minus heterogeneous);

\Delta_{\mathrm{hom}}

is the additional loss attributable to label homogeneity alone (heterogeneous minus flooding). Every

\Delta_{\mathrm{hom}}

is significant at

p<10^{-40}

under Welch’s test.

$C$	payload items	co-signers/edge	normalised	flat	normalised	flat
	coalition’s position		$10\%$ coalition		$25\%$ coalition
$1$	$250$	$1.6$	0.609	0.437	0.373	0.224
$2$	$188$	$2.0$	0.644	0.494	0.425	0.268
$5$	$97$	$3.0$	0.710	0.629	0.530	0.404
$10$	$50$	$4.1$	0.755	0.735	0.612	0.537
$25$	$20$	$5.3$	0.785	0.781	0.722	0.711

Table 15. The coordinated adversary, pooled over the two propositions,

100

seeds per cell. Group size

C

is the number of coalition members sharing one poison item and co-signing its links;

C=1

is the uncoordinated attack of Table 10 . Payload items and co-signers per edge are measured on BRA at the

25\%

coalition. Completeness rises monotonically with

C

in every cell: coordination helps the electorate, not the coalition.

Model component	DDP2P item	Deployment note
poll $\Pi$	motion within an organisation	direct; the organisation supplies the constituency and $\omega_{\mathrm{c}}$
$\mathcal{J}^{+},\mathcal{J}^{-}$	justifications typed by signature polarity	direct
$\mathcal{R}^{\ominus}$	claimed_refutes between justifications	direct; the claim is signed by its author and never adjudicated
$\mathcal{R}^{\oplus}$	claimed_subsumes / includes	direct; more_recent additionally orders revisions
$\omega_{\mathrm{c}}$	constituent record, organisation rules	direct; membership class or shareholding
$E(j)$	votes citing $j$	direct; every vote is a signed item naming the justification it cites

Table 16. Mapping the alternative-based poll of Definition 3.1 onto DDP2P item types. Entries marked new are what a deployment would have to add; everything else already exists.

Deliberative Democracy

Deliberative democracy studies how inclusive, informed public discussion can shape collective decisions and strengthen their legitimacy.

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Open paper AskPDF arXiv

Deliberative polling promises to improve collective decision-making by exposing shareholders to a broad range of arguments before they vote. Yet ensuring that every voter encounters a representative sample of the reason space, the coverage problem, remains an open challenge, particularly at scale and in adversarial or strategically motivated electorates. This paper introduces a way of evaluating solutions using the LLM-based Agentic Bipolar Argumentation Simulator, grounded in a framework which formalises a poll as a six-tuple <Jend, Jopp, Ratt, Renh, VA, VR> of endorsing and opposing justifications, attack and enhance relations, and shareholder- and relation-weights. ABAS simulates N autonomous shareholder agents, each assigned a latent opinion according to desired distributions in [-1, 1], who sequentially vote, choose or author justifications, and optionally submit argumentation-graph links. The simulator implements recommendations that rank existing justifications by their observable endorsement mass. It evaluates the mechanism's success by coverage, namely the fraction of the corpus reason-tag set represented in the K recommendations presented to each shareholder, as a solution to the NP-hard Subsuming Justification Problem. Reported experiments characterise how creativity rate (pown), recommendation size (K), argumentation density (plinks), and population size (N) affect coverage and corpus diversity. In an authenticated electorate where Sybil attacks are impossible and only the relation graph is gameable, we stress-test the scoring with coordinated strategic voting attacks: a tag-flood attack collapses coverage, while author-count relation weighting through a reversed-PageRank rule resists the flood markedly better than uniform weights.

Abstract

Deliberative Democracy

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