Section 03

Reading the numbers

Three figures come back from every run. They are easy to misread in opposite directions, so here is precisely what each one is a function of.

The definitions

Every figure Orakl reports is computed from a single object: the distribution, which is the fraction of agents whose strongest belief, after the last round, sits on each outcome.

Leans
The outcome with the largest share, and that share. Nothing more. It is a vote count, not a probability of the thing happening in the world.
Confidence
One minus the Shannon entropy of the distribution, normalised so that a perfectly even spread scores 0 and a unanimous vote scores 1. It measures how concentrated the vote was. It does not measure how good your input was, how much Orakl knows, or how likely the leading outcome is.Because the entropy is normalised to the number of outcomes, Confidence is only comparable between runs that had the same number of outcomes. A three-way run and a two-way run are on different scales, and the app does not tell you which you are looking at.
Split
One minus the gap between the top two outcomes. A split of 98% means the first and second options finished two points apart. A split of 0% means the leader ran away with it.
Agents
How many agents were in the swarm: 40 on the free tier, 600 on Premium. More agents does not mean more accuracy. It means a finer-grained vote count and a longer-running simulation — the same dynamics, sampled more densely.

All four are displayed truncated rather than rounded, so a vote share of 0.5083 appears as 50%, not 51%. If a bar looks slightly ahead of what the number says, that is why.

The thing nobody tells you: with two outcomes, you are being shown one number twice

Let d be the gap between the first and second outcome. Split is defined as 1 − d. With exactly two outcomes, the distribution is fully determined by d as well — the shares must be (1+d)/2 and (1−d)/2 — so Confidence is also a function of d and of nothing else.This is a property of the definitions, not a bug. But it means that on a two-option question, “Confidence 2%, Split 80%” is not two pieces of evidence agreeing with each other. It is one piece of evidence printed twice in different units.

Two-outcome voteConfidenceSplit
51 / 490%98%
60 / 402%80%
75 / 2518%50%
90 / 1053%19%
99 / 191%2%

Two consequences follow. First, on a two-way question, Confidence is brutal: a 60/40 result — a twenty-point margin — scores 2%. That is not the model being defeatist. Entropy is simply unforgiving about near-even binary votes. Second, the interesting combinations only exist when there are three or more outcomes on the table.

The counter-intuitive combinations

High split with high confidence

Impossible with two outcomes; routine with three. A vote of 50 / 48 / 2 gives a split of 98% and a confidence of 29% — far above the 0% that the equally-tied 51/49 two-way vote scores.

Three-outcome voteConfidenceSplit
50 / 48 / 229%98%
45 / 45 / 1013%100%
60 / 20 / 2013%60%
70 / 15 / 1525%45%
80 / 10 / 1041%29%

What it means. The swarm has done something genuinely useful: it has eliminated an option. The mass collected on two of the three and abandoned the third. The remaining two are tied.

What to do. Treat the run as having answered a different question than you asked. It has told you which option is out, and it has told you that the other two are a real choice that this model cannot make for you. Re-ask with the two survivors and see whether adding context separates them.

Low split with low confidence

A vote of 60 / 20 / 20 has a comfortable forty-point lead — split 60% — and a confidence of 13%. The leader is clear and the reading is still weak.

What it means. The opposition did not consolidate. Nothing beat the leader, but the swarm also never formed a coherent second camp: the objections were scattered across the remaining options rather than pointed at one alternative.

What to do. This is the shape to be most careful with, because the headline percentage looks respectable. A leader that wins against a fragmented field is not the same as a leader that survived a real challenge. Look at the drivers listed underneath and at what the report agent says would flip it. If nothing on that list is something you actually believe, the lead is an artefact of the vocabulary the extractor happened to pick out.

Everything at 100%

Leans 100%, Confidence 100%, Split 0%. This should raise your guard rather than lower it, and it is common on short inputs. A four-word question can produce a single factor, one prior and nothing for anyone to disagree with; the swarm then agrees perfectly and the entropy of a unanimous vote is zero by definition. Example three is exactly this case, shown in full.

The curve underneath

The app also draws “How consensus formed”: the mean belief mass on the leading outcome at the end of each round. It is worth more attention than the three headline figures, because it shows direction rather than a final state.

  • A curve that rises steadily is a swarm consolidating. The argument settled something.
  • A curve that falls — and they do fall; one of our own worked examples descends from 0.548 to 0.504 — means the agents grew less sure as they argued. The initial prior was stronger than anything the discussion supported.
  • A curve that oscillates in the last rounds means the swarm is orbiting a tie rather than approaching one.

Two runs can end on the same three numbers and have completely different curves. If a result matters to you, the curve is where the difference is visible.

What none of them measure

None of these figures is calibrated against anything. There is no historical outcome data behind them, no base rate, no backtest. Confidence is not a probability that the leading outcome will occur, and we do not know what the relationship between the two would be, because we have not measured it and would need real resolved decisions at scale to do so.

The app does let you record what actually happened afterwards, so you can build your own record of when it was right. That record is yours, on your device, and we never see it. We cannot therefore tell you Orakl’s hit rate, and you should be sceptical of anyone in this category who quotes one.