PSI · Public Sector Innovation · LEG v0.12 (calibrated)

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For council leaders Public Sector Innovation · Behavioural Physics

Most council demand isn't random.
It cascades.

One life event — a bereavement, a discharge from hospital, a benefit sanction — triggers a chain of downstream council touches that costs more than the original event ever did. PSI applies a Behavioural Physics model to make the cascade visible, so you can see where targeted prevention pays back before you spend the budget.

The model

259 edges

A Life Event Graph linking 42 council-relevant trigger events to 92 service nodes, with 59 compounding antecedent-to-antecedent pathways and 10 service-to-antecedent feedback edges. Calibrated against UK empirical incidence.

The simulation

100k people

A Monte Carlo run over an HSV-conditioned synthetic population gives you authority-specific 36-month cost forecasts, not national averages.

The decision

27 interventions

An evidence-based library of UK interventions, ranked on cost-effectiveness for your authority's cohort — primary prevention and tertiary disruption both modelled.

What you'll see in the next four pages

Choose your authority sets the population, deprivation, and incidence profile the simulation runs against.

See the cascade plays the 36-month event cascade for that authority's population — 100,000 simulated lives, each with their own HSV vector, each triggering events at HSV-conditioned rates.

Spot the patterns mines the simulation for the recurring chains and loops driving the largest share of cost.

Plan interventions lets you stack evidence-based interventions and see how they bend the cost curve — with full downstream cascade savings credited, not just direct service avoidance.

Why this is different to a normal council dashboard

Traditional cost analysis treats each service line as independent. PSI's model treats them as one connected system — the way they actually behave in a person's life.

This matters because primary prevention only looks viable when you can credit the full downstream chain it disrupts. A £1,400 carer's respite intervention isn't competing with one ASC service; it's competing with the cared-for person's MH crisis, the carer's own MH risk, the cascade into A&E and employment loss, and so on.

Model basis: LEG v0.12 — 259 edges over 42 antecedents and 92 service nodes. Includes 59 antecedent-to-antecedent compounding edges (batches 29 + 30), 10 service-to-antecedent feedback edges (batch 31), and a calibrated baseline pass so simulated antecedent firing rates converge with empirical UK population figures.

Choose your local authority

The model runs against your authority's specific population size, deprivation profile, and antecedent-incidence multipliers. Switching authority re-tunes every number you see on the next three pages.

Local authority

Adult population

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Deprivation profile

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Region

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Modelled 36-mo public cost

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Pick an authority above to see its profile. If your authority isn't listed, the closest deprivation-and-size peer will give you a directionally accurate result.

Cascade and cost for 100,000 people over 36 months

Each simulated person has an HSV vector that determines both which antecedent events they experience (rates are HSV-conditioned Poisson) and how those events cascade through council services.

0.0 mo

Sample Speed Recurrence

Simulating people…

starting

36-month cascade cost

Public sector total

£0

LA-borne share

£0

People touched— Avg cost / touched— Top 5% drive— Total events—

Per-node cost ↓ public £

Node	Public £	LA £
Press play.
Total	£0	£0

By service portfolio

Portfolio	Public £	LA £
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Per-person 36mo cost — long tail log £ axis

Visual key

resilient person

average person

precarious person

Recurrence edge

Housing

Mental health

Substance

Adult social care

Domestic abuse

Welfare

Next step

Now mine the simulation for recurring patterns

The cascade you just watched produces thousands of distinct trajectories. The next page surfaces the chains driving the largest share of cost and the loops where people re-enter the system instead of resolving.

Spot the patterns

The simulation produces thousands of distinct trajectories. These two panels surface the ones that matter — the recurring chains that drive the largest share of cost, and the loops where a service handoff sends people back to an earlier service instead of resolving the cascade.

↗

How to use this view. Pick a chain or loop from the lists on the right — the 3D graph below highlights its nodes and edges, and animates particles along the path. Rotate the graph by click-and-drag, zoom with the wheel, and press Clear selection to reset.

Select a chain or loop on the right

The full LEG is shown below. Selecting a pattern highlights its nodes and edges and animates HSV-mix-coloured particles along it.

Trigger Housing MH Substance ASC DA Welfare forward recurrence (curved) resilient particle average precarious click + drag to rotate · scroll to zoom · right-click + drag to pan

Top chains

Recurrence loops

Pattern details appear here when you select a chain or loop.

So what?

The top chains and loops are where intervention pays back hardest.

The chains list is sorted by total cost contribution. The top 3 chains typically account for around 30–40% of all cascade cost in a 36-month simulation. Disrupting a single high-frequency chain — even with a low success rate — usually saves more than running a high-success intervention on a rare pathway.

Loops are the recurrence engines: each repetition charges the cost again. A loop with average traversal frequency of 2.5 and a cost of £8,000 per cycle represents £20,000 of avoidable cost per person stuck in it. Look at which loops connect to your intervention targets on page 5.

Next step

Now plan interventions against these patterns

Activate evidence-based interventions and see how they bend the cost curve. The cost-effectiveness frontier shows which combinations pay back inside 36 months for your authority's cohort.

Plan interventions

Activate interventions from the library on the right. Each one reduces an antecedent rate (primary prevention) or disrupts a specific cascade edge (tertiary). The frontier below shows you which combinations are net-positive for your authority — anything above the dashed diagonal pays back inside 36 months.

v0.12 CALIBRATED MODEL

The cascade graph includes 59 antecedent-to-antecedent edges (compounding shock, economic-stress, health, crime/housing, and substance cascades) plus 10 service-to-antecedent feedback edges (TA → MH crisis, MHA detention → job loss, etc.). Primary-prevention interventions like Carer's Respite, IAPT, Citizens Advice debt support, and Through-the-Gate now credit the full downstream compounding cascade — not just the immediate service avoidance.

Receiving-antecedent baselines have been down-calibrated so simulated firing rates converge with empirical UK population figures. Most rates now land within ±15% of ONS / PHE / DWP baselines. The acute MH crisis rate is the one residual: cascade contribution still exceeds the empirical baseline somewhat, indicating either slightly hot attributable-risk values or — more likely — that the published incidence figure under-counts cascading crises. Treat MH-driven savings as a directional indicator rather than a precise figure.

Cost-effectiveness frontier

Available intervention (greyed = not active) Active primary prevention Active cascade disruption Break-even line (savings = cost) Your current portfolio

Each grey dot is an available intervention plotted at its (cost, savings) position when deployed alone at typical LA-scale. Click any dot to activate it — the dot lights up in colour and the blue "Your portfolio" marker moves to reflect your new combined spend and savings. The dashed green diagonal is the break-even line: any intervention or portfolio above it returns more in downstream savings than it costs to deliver. The vertical barometer on the right shows what percentage of the theoretical maximum savings (across the whole library) your active portfolio is capturing.

Computing single-intervention scenarios across the library…

starting

Prevention intervention library

Twenty-seven UK evidence-based prevention interventions. Activate any combination, set how many cases per year you intend to treat, and watch the projected effect on this LA's 36-month cascade cost. Each intervention has a real published cost-per-case and a published success rate; sources are cited on every card.

20 interventions in library H RCT or large-scale evaluation M Strong observational / SROI L Limited evidence

Sort Filter

Projected 36-month savings (selected LA)

£0

Move any slider below 100% to start modelling

Baseline public ££0 After intervention£0 Baseline LA ££0 After intervention£0

Invest-to-save calculator

Intervention cost over 36 months (£, auto from active library items)

Payback period

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36-month ROI

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Payback = months for savings to equal intervention cost (assumes savings accrue linearly). ROI = (savings − cost) / cost over 36 months. Public-sector basis.

Service portfolio impact

Adjust sliders to see per-service impact

Take it to the CEO

An actionable plan for the interventions you've selected. Set each one's start month, see how spend phases month-by-month against the lagged benefit accrual, and produce a printable A4 exec summary your CEO can take to a cabinet meeting.

LA-only net position at M36

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Public-sector net position at M36

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Payback month (LA)

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Cumulative LA cashflow crosses £0

Total LA spend over 36 months

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Phase each intervention

Pick the start month for each active intervention. Spend begins from that month; benefits start accruing after the cascade-lag delay.

Cashflow over 36 months

Red bars = monthly spend, green bars = monthly benefit. The yellow line tracks cumulative net cashflow — when it crosses zero, the plan pays back.

LA-only cashflow

Public-sector cashflow (LA + NHS + DWP + MoJ)