Poliwave's Methodology

There are two classical ways to convert a national swing into a riding-level projection, and each one breaks in a different way.

Proportional swing multiplies every riding by the same ratio. If a party doubles nationally, every riding doubles too. This is fine most of the time but breaks during big swings in either direction. A party that was already at 55% in a riding has nowhere to go when you double it, and the formula tries to push it past 100%. More damagingly, when a party collapses nationally (think NDP 2025 going from 17.8% to 6%), pure proportional brutalises strongholds — Edmonton Strathcona's 60.7% gets scaled down to 20% even though incumbent personal vote and local brand strength should preserve much more than that.

Uniform swing adds the same number of points to every riding. If the party drops 10 points nationally, every riding drops 10 points. This breaks the other way: a party at 3% in a riding drops to negative 7%, which is not a thing. Pure uniform also has the opposite collapse problem: a riding where the party had almost no presence keeps a non-zero share that's basically noise.

Poliwave's projection formula takes the geometric mean of both — it multiplies the two predictions together and takes the square root. Each prediction is floored at zero first so the inputs to the square root can't be negative:

The geometric mean is the natural average for percentages. It always sits between the two predictions, and it gets pulled toward whichever one is smaller. That single mathematical property fixes both classical failure modes at once: when proportional explodes high, the smaller uniform value pulls the answer down; when uniform crashes to zero, geometric mean returns zero too (because square root of anything-times-zero is zero), which is the correct answer for a riding where the party has effectively vanished.

Every riding goes through the same ordered set of steps. The swing formula above is one of them. The others clean up the input to the formula and make the output line up with everything else the model has to respect.

1. Input parsing. The model loads each riding's previous result, the geographic hierarchy (which riding belongs to which sub-region, province, region), and any referendum results for the target election's redistribution (rep_order). Your hierarchical input is flattened into a lookup so each riding picks the most specific target that applies to it.
2. Historical normalisation. Missing or unreliable prior results get filled in. A party that did not nominate a candidate at all (a recent Canadian example: Conservatives in Québec Centre, 2025), or that ran with less than 20% of its own national share for the cycle (the cutoff that separates a real campaign from a late-withdrawal residue), gets rebuilt by one of three methods described in the next section. This step runs on whatever prior-cycle baseline the database holds for the riding, including transposed results from older boundaries (a 2025 federal projection's main baseline is the 2021 result transposed onto the 2023 rep_order, for instance).
3. Swing projection. The core formula runs on every riding and every party. Special cases handle brand-new parties and parties running nationally but absent from this riding.
4. Simple normalisation. The riding's projected percentages are rescaled to add up to 100%. Anything negative is set to zero.
5. Vote flow. Loss-only redistribution. When a party is projected to lose share, the lost share is handed to other parties according to a flow matrix you supply.
6. Vote intake. Vote transfers that don't depend on whether a party is winning or losing. The formula is in the redistribution section below.
7. Tactical voting. Strategic defection in FPTP races, scaled by how close the local race is. Two rule types: block-target voting (anti-X coordination) and the top-two squeeze (wasted-vote logic). This stage is off by default in the formal projections published on the site and is enabled only when you turn it on in the interactive simulator.
8. Regional adjustments. Manual knobs. You give the model two tables, one for additive shifts and one for percent multipliers, organised by level (subregional, subnational, regional) and by party. Each cell is the change you want applied at that level for that party. The model just applies what you wrote; nothing is auto-computed here.
9. Demographics. Per-category adjustments scaled to the party's existing support. You set a boost for a (party, demographic) pair; the model multiplies it by how far the riding deviates from the national average for that demographic and by the party's current vote share in the riding, so the effect can't blow past what the party actually has to move.
10. Incumbent boost. An automatic 5% multiplicative boost goes to the party of any candidate identified as a running incumbent in the riding (sitting MP seeking re-election). A symmetric 5% deboost goes to the previous-winner party when the sitting MP is known to be retiring or otherwise not on the ballot. Both magnitudes are calibrated from a backtest sweep across 38 Canadian elections since 2000; see the dedicated section below.
11. Riding boosts. Per-riding manual overrides, either additive or multiplicative. Useful for unusually strong or weak local candidates beyond the auto-incumbent effect, well-known local figures, or one-off scenario tweaks. User boosts stack on top of the auto-incumbent boost.
12. Hierarchical normalisation. The rescaling step. Every riding is rescaled level by level (subregional first, general last) so the vote-weighted average at each level matches your input for that level. The general (national) level runs last and is the binding rule the result has to respect.
13. Threshold capping. Damps any party that's running hot in a riding compared to its cohort. When the projected share exceeds a multiple of the regional or national average (default cap: 1.5× that average), the excess gets reduced by a set rate (default 50%). The riding is then renormalised to 100%, and hierarchical normalisation is re-run so the capping doesn't break the geographic totals. This isn't a small-party squelch; it applies to any party that runs hot.
14. Aggregation. Riding winners are picked, seat totals are added up by party, and geographic summary tables are built for each level of the hierarchy.
15. Output. Everything is packaged into the JSON response used by the website and by the Monte Carlo layer further down this page.

Inside that history window, the most important prep step is filling in missing or unreliable prior results. A naive model would take "the party got 0% here" at face value and project from that. Poliwave does not, for two reasons.

The first reason is candidate withdrawal. A party might just not have nominated a candidate at all in the last cycle. There are real Canadian cases: the Conservatives did not run a candidate in Québec Centre in 2025, so the prior result is structurally zero, and treating it as a real voter preference would be wrong.

The second reason is late withdrawals that still leave a name on the ballot. The 2019 Brexit Party stand-down in Conservative-held UK seats is the classic example, but the same thing happens in Canada when a candidate withdraws after the nomination deadline. The resulting tenths of a percent look like a vote share, but they don't reflect a real campaign. Either way, this needs to be cleaned up before the swing formula sees the baseline.

When the model has to fill a baseline in, it picks one of three branches depending on what data is available. Note that transposed prior results (for example the 2021 federal result mapped onto the 2023 rep_order) are treated as the real prior result for the riding and go through this stage like any other baseline. They're the main input the projection runs on, not an exceptional case.

Rebuilt baselines are not treated as if they were real. Each baseline carries a confidence weight depending on where it came from: real database results are 1.0, branch-1 reconstructions are 0.7, and the branch-3 regional fallback is 0.4. Before the swing formula reads the baseline, low-confidence baselines get pulled toward the regional mean by a weighted average:

The effect is a careful pull toward the average. When the model trusts the baseline, it respects the riding's individual character. When it doesn't, the riding behaves more like its regional cohort. That keeps a single noisy or guessed number from contaminating the rest of the pipeline.

Voters move between parties in three different ways, and Poliwave handles each one separately. The three run in order, with each one working on what the previous one produced.

Demographic effects in real elections are relative, not absolute. If a party does ten points better with renters, that doesn't mean it picks up ten points everywhere. It picks up ten points in ridings that have a lot more renters than the national average, almost nothing in average ridings, and loses ten points in ridings with way fewer renters than average. Poliwave handles this directly. For each (party, demographic) boost you set, the model multiplies your boost by how far the riding deviates from the national average for that demographic, and by the party's current support in that riding:

The deviation term is what makes the adjustment relative. Above-average ridings get a push proportional to how far above average they are; average ridings barely move; below-average ridings get pushed the opposite way. Multiplying by the party's current support is what keeps the formula honest: a party with no vote share in a riding gets no demographic shift (a 0% party times anything is still 0), and a party already strong in the riding has more vote share available to move. A party sitting at 3% can drift by a few tenths of a point per category; a party at 30% shifts ten times more in absolute terms but the same in relative terms. That self-bounding shape is what stops a small input ever amplifying into an unintended seat flip downstream.

Incumbent candidates outperform their party's swing. The pattern is robust across systems and shows up in almost every academic study of personal-vote effects: name recognition, constituency casework, media presence during the prior term, and a ready-made local volunteer base all add up to a few percentage points of advantage that pure party-level swing math will miss. The flip side is sophomore-surge loss: when a sitting MP retires, the same seat loses the personal vote that helped prop it up, and the party usually slips back toward its normal baseline.

Poliwave applies both effects directly. After demographics and before any user-supplied riding overrides, the model classifies every riding into one of three states and adjusts the projected vote share of the relevant party:

• Incumbent running. Multiplicative +5% boost to the incumbent's party.
• Incumbent retiring. Multiplicative −5% deboost to the previous-winner party. The seat may still be safe, but the personal vote is gone.
• No prior history available. No adjustment.

In the formula, $R_{p,i}$ is party $p$ 's raw baseline result in riding $i$ , so $w$ picks out the previous winner; $P_{w,i}$ is that party's currently-projected share after the swing and all the redistribution steps above. The boost factor (1 ± b/100) is positive for running incumbents and negative for retiring ones. The riding is then renormalised back to 100% so the within-riding shares still sum cleanly, and the broader hierarchical reconciliation downstream re-anchors regional and national vote-weighted averages to the user's input — so the boost shifts the within-region distribution, not the regional totals.

Identifying the incumbent

Each riding is classified by walking a priority cascade. The model looks at the election we're projecting to (when its candidate data is in the database) and tags each riding using the first signal that fires:

1. Explicit incumbent flag. A target-election row marked isIncumbent = true. Set when a sitting MP appears on the next ballot. Boost their party.
2. Candidate-name match. If no flag was set, compare candidate names between the baseline election and the target. A target candidate whose name also appears in the same riding's baseline ballot is treated as an incumbent. Catches cases where the flag was missed during data entry.
3. Retiring fallback. When the baseline winner's candidate name does NOT appear in the target's candidate list, the seat is marked as a retiring-incumbent case and gets the negative deboost.
4. Baseline-winner heuristic. When no target candidate data is available at all (live forward projection of an upcoming race), the model falls back on the party of the baseline winner and applies the positive boost only. Without target data the model can't tell running from retiring, so the deboost arm is disabled for these runs.

Parties classified as "Other," independent, or Speaker are excluded. The first is a mathematical lump rather than a real party with a sitting MP, and the latter two have their own special-case handling elsewhere in the pipeline.

Manual riding boosts in the next step stack on top of this. If you know a specific candidate is exceptionally strong or unusually weak beyond what the party-level incumbency boost captures, you can add a per-riding additive or multiplicative adjustment that runs after the automatic step. The two stack rather than override: the auto-boost lifts (or trims) the projected winner first, your manual boost adjusts further on top.

Every projection has to answer a question you asked, like "what does the country look like if the Liberals are at 26% nationally and the Bloc is at 30% in Quebec?" The reconciliation step is what makes those targets actually stick. For each geographic group at each level, the model takes the current vote-weighted average of the group, compares it to your target for that group, and multiplies every riding in the group by one correction factor:

The $v$ in the formula is the riding's total vote count. It weighs each riding's contribution to the group average, so larger ridings have more influence. The four levels run in this fixed order: subregional first, then subnational, then regional, then general (national) last.

This top-down setup has a useful property. The geographic variation that earlier steps built in is preserved, because every rescale is just multiplication: if a riding was double its regional average before reconciliation, it's still double afterwards. Only the absolute level changes. That's what lets the model honour any national target without flattening the riding-by-riding texture that makes the projection useful. It also means that if you genuinely want one province at 10% while the country is at 50%, you have to drop one of the inputs. The two don't agree with each other, and the model trusts the broader target.

This also matters when pollsters get their regional weighting wrong. A pollster's regional crosstabs don't always weight back up to the national headline they reported. If you fed those inconsistent regional numbers in as hard ceilings, the national total in the projection would drift away from the topline. Because Poliwave runs the national level last and rescales whatever the regions produced, the topline you trust the most stays the binding number, and a regionally mis-weighted poll still produces a sensible projection.

Getting a single point estimate is the easy part of a forecast. The hard part is what could happen around it. For formal projections, Poliwave runs Monte Carlo on top of the base projection (40,000 draws by default, more if set higher via the CLI) using a correlated error model. Polling error is split into three pieces: a national piece that moves every riding the same way, a regional piece that moves ridings inside one region together, and a per-riding piece that's independent and whose size depends on the riding's population.

The split exists because real polling misses aren't independent across ridings. They're usually systemic and regional. If you treated every riding as an independent draw, the confidence intervals would be way too narrow and the seat distributions would be too tight around the centre. The correlated split gives back the realistic spread an honest forecast needs.

The third piece, the per-riding term, has its variance scaled inversely by the riding's elector count. A small northern riding with 35,000 electors really is noisier than a Toronto-area riding with 110,000, because a smaller electorate gives more leverage to single events (a popular local candidate, a scandal, a local issue):

${\sigma }_0$ is the calibrated noise level at the reference population $N_{\mathrm{ref}}$ (the median riding size in the jurisdiction), and $N_i$ is the riding's own elector count. This is what gives small ridings wider win-probability ranges than large ones, and any honest forecast model has to behave this way.

What the simulation actually produces:

• Per-riding win probabilities and 95% confidence intervals for every party.
• Seat distributions at the regional and national level.
• Government formation probabilities: majority, minority, plurality, hung. Each gets its own simulated frequency, based on your inputs and the correlated error structure above.