VOL. 06 / Research
The Threshold Cliff
A bachelor thesis that treated an election as a forecasting problem. The interesting uncertainty was never in the polling — it was in a rule where a fraction of a point either side of a threshold changes the answer completely. Tax bands, covenants and volume tiers behave the same way.
Quick read
Research · forecasting
Research- The problem
- When an outcome passes through a threshold, it is the threshold that must be modelled.
- Who it is for
- A methodological audience. It is published here as evidence of how I handle forecasting under structural rules, not as political analysis.
- What you receive
- Method, data provenance, and no accuracy claim, because none was published
- Evidence status
- Research evidencePublished method; no measured forecasting accuracy is claimed.
- Main limitation
- No held-out accuracy is published, so no predictive performance is claimed.
Volume VI · Research · forecasting
The Threshold Cliff
When an outcome passes through a threshold, it is the threshold that must be modelled.
Research
Investigative work with a published artefact. Not deployed, and not in use by anyone.
The problem
Vote-share polling does not answer the question people actually ask about an election. Under D’Hondt allocation with an electoral threshold, small changes in share produce large, discontinuous changes in seats, and the interesting uncertainty lives in that conversion rather than in the polling.
Who it is for
A methodological audience. It is published here as evidence of how I handle forecasting under structural rules, not as political analysis.
Context
My bachelor thesis in Economics, Management and Computer Science at Bocconi, completed in 2023. It is research, and it has not been maintained since.
My role
Sole author: data collection, modelling and the written thesis.
Data provenance
Published historical results from the Supreme Election Council (YSK), demographic and socio-economic indicators from the Turkish Statistical Institute (TurkStat), public polling, and administrative boundary shapefiles.
Constraints
Province-level published data only, and a polling record whose historical accuracy is itself uncertain — which pushes the work toward modelling the conversion rules rather than trying to out-predict the polls.
Approach
- Assemble province-level historical results and align them with demographic and socio-economic indicators.
- Model vote share at province level rather than nationally, since seat allocation happens per constituency.
- Apply the actual seat-allocation rules, including the electoral threshold, so the discontinuities are reproduced rather than smoothed away.
Approach
- Examine where the forecast is most sensitive — which is concentrated in a small number of provinces near allocation boundaries.
Decisions that mattered
- Forecast seats through the allocation rules rather than regressing on seat counts directly.
- Seat counts are a deterministic function of vote shares and rules. Learning that function from a handful of past elections would be fitting noise where the rule is already known exactly.
- Kept the analysis at province level.
- A national vote-share error of one point matters enormously in some provinces and not at all in others.
Figure
Figure A chart showing seat allocation as a function of vote share, with a sharp step at the electoral threshold: parties below it receive no seats, and parties just above it gain a disproportionate number. The relationship between share and seats is flat in the middle of the range and steep near the boundaries.
How a small change in vote share moves seats under threshold-based allocation. Drawn from the thesis method; an illustration of the mechanism, not a forecast.
How it was evaluated
The repository documents the method and the data sources; it does not report a held-out accuracy figure. No performance claim is made here because none is published, and inventing one after the fact would not be a measurement.
Results
No performance figure is published for this project, so none is claimed.
What was delivered
- Notebooks covering vote-share estimation, seat allocation and the presidential race.
- An assembled province-level dataset joining electoral, demographic and socio-economic sources.
- The written thesis.
What it changes in practice
The transferable point is about structure, not politics: when an outcome passes through a rule with cliffs in it, the forecast has to model the rule. The same reasoning applies to tax bands, covenant tests and volume tiers.
Limitations
- No held-out accuracy is published, so no predictive performance is claimed.
- Built for one election under one set of rules; it is not a general election model.
- Not maintained since 2023.
Human review
Research output, read as such. Nothing here is a prediction offered for decision-making.
Source material
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