6 Conclusion
This thesis set out from a deceptively simple question: when a sortition algorithm satisfies every quota it is given, does the panel it returns actually represent the population it was drawn from? The literature reviewed in Chapter 2 showed that a sustained line of algorithmic development – from LEGACY through MaxiMin and MiniMax to LexiMin and Goldilocks – have answered an adjacent but different question extensively: how to make individual selection probabilities as fair and as robust to manipulation as possible. What none of these methods do is stratify, constrain, or even check their output against the combinations of traits that make up a population’s intersectional structure. The implicit assumption running through the field has been that marginal fairness, achieved at the level of each demographic category independently, is sufficient to carry intersectional representativeness along with it for free.
Chapter 3 and Chapter 4 tested that assumption directly, and found it does not hold. Across every simulated condition – independent or associated populations, equal-chance or age-skewed response – effectively every feasible panel Panelot’s LexiMin implementation could return showed an age-tenure relationship significantly different from its own survey sample, at a rate roughly an order of magnitude above what simple random sampling of the same size produces. Strikingly, this held even in the independent population, where there was no true association for a panel to represent in the first place: the distortion is a property of the quota mechanism itself, not of any one population structure or non-response pattern. Panels built to satisfy marginal quotas on age and on tenure separately were, time and again, blocky and uneven in their joint composition – a pattern invisible to the pie charts and bar charts that typically accompany reported panel composition in practice (Section 4.1), and invisible, more fundamentally, to any quota system that only ever looks at one trait at a time.
Chapter 5 responded to that finding with Intersection Inspector: a tool aimed at closing the gap between what current selection algorithms guarantee and what practitioners actually need to know before convening a panel. By placing mosaic plot comparisons, marginal bar charts, and formal association tests directly in a practitioner’s hands – alongside panel browsing, random and weighted-random selection, and an under-representation threshold – the app turns the previously invisible final step of the sortition pipeline into something inspectable, without requiring a statistics background to use.
6.1 Framework and recommendations
Taken together, these chapters suggest a straightforward recommendation for practitioners and tool-builders alike: marginal quota satisfaction should be treated as necessary, but never sufficient, evidence of a representative panel. A panel that hits every category count it was asked to hit can still systematically misrepresent how those categories combine in the community it is meant to reflect, and nothing in the quota-setting or selection process as currently practised will achieve that on its own.
In practical terms, this points toward a layered framework for panel evaluation. First, quota-based selection (LexiMin, or in future, Goldilocks) remains the right tool for ensuring fair and robust selection probabilities at the marginal level – this thesis does not dispute the value of that work, only its sufficiency. Second, an intersectional check, of the kind Intersection Inspector performs, should sit between panel generation and panel convening, so that a practitioner can see whether a panel’s joint trait structure plausibly reflects its sample before members are contacted, rather than discovering a skew only once deliberation is already underway. Third, where a specific intersectional combination is known to matter for an engagement’s context – a particular minority subgroup, say – this thesis’s results suggest that relying on marginal quotas to deliver it incidentally is optimistic at best; deliberate joint-quota constraints, or supplementary recruitment targeted at that intersection, are more defensible routes than trusting the selection mechanism to produce it as a byproduct.
6.2 Limitations
Several limitations bound how far these findings should be read. The simulation used two categorical variables – age and tenure – chosen for their resemblance to variables genuinely used in sortition practice, but real panels are typically built against three, five, or more demographic categories simultaneously; the discrepancy documented here is expected to compound, not relax, as the intersectional space grows while panel size stays fixed. However, that expectation was not itself tested at higher dimensionality (Chapter 3). Likewise, response rates were deliberately elevated well above what civic lotteries typically see in the field, to keep respondent cells populated enough to isolate the algorithm’s own behaviour; this makes the reported distortion a conservative, best-case estimate rather than an upper bound, and the association strengths introduced into the simulated populations were fixed at values chosen for visibility rather than drawn from, or validated against, any specific real-world dataset (Chapter 3).
Intersection Inspector itself carries its own, openly acknowledged constraints (Section 5.3). It inspects two variables’ joint structure at a time, rather than the full multivariate intersection a panel’s representativeness ultimately rests on. It also sorts uploaded trait levels alphabetically, which can misorder ordinal variables and make an association harder to read by eye – though the underlying statistical tests remain valid regardless of level order. Both are deliberate trade-offs in favour of interpretability for non-specialist users, but they mean the app diagnoses the problem this thesis identifies more thoroughly than it solves it outright.
6.3 Future research
A natural next step is extending the simulation framework beyond two variables, to establish whether, and how severely, the intersectional distortion observed here scales with additional demographic categories – and whether it does so uniformly or concentrates in particular combinations with many trait levels. The Goldilocks algorithm, not yet publicly available at the time of writing, is also worth revisiting once released: it addresses a different problem (robustness to manipulation) to the one this thesis raises, but it remains an open question whether its joint handling of selection-probability ceilings and floors incidentally improves, worsens, or leaves unchanged the intersectional preservation documented here. More broadly, this thesis’s central finding motivates a more direct line of work: selection methods that explicitly incorporate joint, intersectional constraints alongside marginal quotas, rather than treating intersectionality purely as something to check for after the fact. One emerging example is Diversimax (Matar 2025), which uses mixed integer programming to select panels that explicitly minimise imbalance across every intersectional combination of demographic traits, rather than optimising selection probabilities at the marginal level alone; it is not evaluated in detail here, since it has yet to see the kind of practitioner adoption LexiMin has. However, it is also worth treating cautiously rather than as a straightforward replacement: optimising for intersectional balance alone, without also bounding how unequal individual selection probabilities can become, risks reopening the same extreme-probability and manipulation vulnerabilities that motivated MaxiMin, MiniMax, LexiMin and Goldilocks in the first place – a panel could end up intersectionally balanced only because some individuals were given a far higher selection chance than others to fill sparse cells. Reconciling intersectional balance with that fairness guarantee looks like the more productive target than optimising for either alone.
On the tooling side, a practical next step is packaging this thesis’s LexiMin implementation as a proper R package and integrating panel selection directly into Intersection Inspector, rather than requiring a practitioner to generate a lottery file via the separate Panelot.org interface before uploading it to the app. Collapsing today’s two-tool workflow into a single environment – covering both panel generation and intersectional evaluation – would remove a point of friction for practitioners, and would make it straightforward to extend the same integration to Goldilocks or Diversimax as those become more broadly available.
6.4 Closing remarks
It is worth being plain about what this thesis is, and is not, arguing. The fairness and robustness advances surveyed in Chapter 2 are genuine achievements, and nothing here suggests abandoning them. LexiMin’s maximisation of selection probabilities, and Goldilocks’ guard against manipulation, solve real problems that mattered enough to motivate years of concentrated algorithmic work. But a selection mechanism being fair is a different property from the panel it produces being representative, and this thesis has tried to show, explicitly, that the gap between the two is not merely theoretical. Optimising who gets a chance to be selected is not the same question as asking who, collectively, ends up involved – and whether the particular mix of people assembled actually reflects the community whose voice the process claims to amplify.
Representation, in other words, is not just a matter of getting the proportions right on each axis taken separately; it is a matter of getting the people right, in all the ways their identities and circumstances combine. A panel can be perfectly fair by the numbers and still quietly leave an entire slice of a community’s lived experience unheard, simply because no one checked whether the categories were ever meant to be looked at together. If sortition’s promise is a seat for everyone, a fair lottery is not the end of the question – it is only the beginning. The real test is who actually ends up on the panel, with their thoughts and feelings heard. So before the next panel is called fair and finished, it is worth pausing to ask: am I in the room?