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No More Awkward Silences with Table Talk Tuning

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Martin Butler · Mikael Z. Lagerkvist
ModRef 2026

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Kungasalen prepared with round tables for the wedding reception
Kungasalen prepared with round tables for the wedding reception

What will guests talk about?

layout: columns

Structurally feasible

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The room works

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  • capacities hold
  • together/apart requests hold
  • table balance stays within bounds

Socially acceptable

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The table works

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  • each guest has shared ground
  • a strict majority can sustain the topic
  • protect the weakest-served guest first
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Strict majorities at Table 19

figureInterest-score matrix for five guests and six topics at table 19, with the strict-majority floor for every topic
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Different topics for different guests

figureThree supported topics at table 19: jazz gives Mina, Theo, and Leila a score of seven; food gives Oskar five; garden gives Petra four
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Structure first; conversation breaks ties

figureFive-level lexicographic objective: minimise total slack, maximum slack, and imbalance, then maximise minimum and total guest interest
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The model stays close to that definition

display math
b(t,k)=strict-majority order statistic of the seated guests’ scoresb(t,k)=\text{strict-majority order statistic of the seated guests' scores}
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q(g,t)=max⁡kmin⁡{b(t,k),s(g,k)}q(g,t)=\max_k \min\{b(t,k),s(g,k)\}
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  1. Take the strict-majority floor for each topic.
  2. Clip it by the guest's own interest.
  3. Keep the best supported topic.
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Detail: one scalar preserves all five levels

code: minizinc
1int: total_interest_weight = 1;2int: min_interest_weight = total_max_possible_interest + 1;3int: imbalance_weight =4  (max_possible_interest + 1) * min_interest_weight;5int: max_slack_weight =6  (max_possible_imbalance + 1) * imbalance_weight;7int: total_slack_weight =8  (max_max_slack + 1) * max_slack_weight;910var int: goal =11    total_slack * total_slack_weight12  + max_slack * max_slack_weight13  + total_imbalance * imbalance_weight14  + min_interest_penalty * min_interest_weight15  + total_interest_penalty;
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Each base is one larger than the complete range of all lower-priority digits.

Step 0 of 3
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MiniZinc Model Results

figureOn the MiniZinc model, Gecode LNS is strongest for anytime quality, Huub is the strongest base-model solver, and Huub and CP-SAT prove the most instances
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Sequential optimisation in native Gecode?

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Optimise one component. Prove it. Fix it. Move to the next.

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The objective is lexicographic; why not make the native search lexicographic too?

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Sequential search makes the conversation terms wait

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Levels 1–3

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Optimise · prove · fix

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  • total slack
  • maximum slack
  • imbalance

Levels 4–5

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Still waiting

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  • minimum interest
  • total interest
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A 60-second budget can disappear in the first three proofs.

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Scalar and direct lexicographic usually win

figureComparison of scalar, direct lexicographic, and sequential objective handling on the same native Table Talk Tuning model
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Model shared ground; search decides how far we get

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  • Model shared conversational ground without pretending to predict conversation.
  • Use Gecode LNS for strong seatings; Huub and CP-SAT help prove them on the standard model.
  • Native Gecode shows that sequential optimisation is natural—but not automatically best.
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