Allais common-consequence effect
Also known as: Common consequence effect
Adding the same outcome to two gambles shouldn't change your ranking — but it does.
What it means
The common-consequence effect is the structural mechanism behind the Allais paradox: preferences between two prospects reverse when a common outcome shared by both is altered, even though the independence axiom says such a shared consequence should cancel and leave the ranking intact. In the classic version, shifting a common 89% chance from a positive payoff to zero turns a safe choice into a risky one. The reversal arises because the change moves one option across the boundary of certainty, where decision weights are most distorted. It is decisive evidence against expected utility's independence axiom and a primary target that rank-dependent and prospect theories were built to accommodate. Distinguishing it from the related common-ratio effect sharpens exactly which axiom each anomaly violates.
The arithmetic of the reversal
Allais's numbers make the switch visible. Choice one: a certain 1 million, or a gamble paying 5 million with 10 percent, 1 million with 89 percent, nothing with 1 percent. Most take the certain million. Choice two: 1 million with 11 percent, or 5 million with 10 percent. Most now take the second. Yet choice two is choice one with the shared 89 percent branch switched from 1 million to nothing. The independence axiom, the lottery-space cousin of Savage's sure-thing principle, says an outcome delivered identically by both options cannot bear on the ranking, so it cancels and both choices should match. In the Marschak-Machina triangle the two sit on parallel lines that expected utility must answer alike.
Why it happens
Kahneman and Tversky's answer is the certainty effect: the step from 99 to 100 percent feels larger than the identical step from 10 to 11 percent, because decision weights are steep near the endpoints and flat across the middle. Choice one parks an option on the certainty boundary; choice two loads both with a large chance of nothing, removing boundary and premium together. That is the textbook account, and it is the one the definition above records, but it is now contested rather than settled. A rival reading runs through anticipated regret: gambling away a sure million creates a sharp regret that choice two never manufactures. A third is blunter: people avoid the branch paying zero. Incekara-Hafalir, Kim and Stecher separate the two and find support for this zero effect, with weak to nonexistent evidence for certainty. The accounts predict alike in the classic problem, which is why untangling them took decades.
What the evidence shows
Blavatskyy, Ortmann and Panchenko pooled 81 experiments from 29 studies and found the paradox fragile, not constant. It appears reliably when payoffs are large and hypothetical, when the middle outcome sits close to the top, and when lotteries are shown as probability distributions rather than compound form; it tends to reverse when probability mass splits evenly between the worst and best outcomes. Huck and Müller took it to a representative Dutch sample and found violation rates about 15 percentage points higher than in the matched student lab, much of it systematic, with a large share of the non-lab violations likely stemming from unfamiliarity with million-scale sums. Millroth, Nilsson and Juslin ran a conceptual replication of the 1979 problems on about 1,800 people: the set replicated poorly, and the rate rose with numeracy, awkward for anyone dismissing the reversal as confusion. Their low-numeracy participants instead leaned on a cautionary non-compensatory rule, minimizing the risk of the worst possible outcome — which is the zero effect of the previous section arriving by an independent route, from a sample selected for numeracy rather than a design built to separate the two accounts.
Related but distinct
The common-ratio effect is the sibling most often conflated with it. There you scale both options' win probabilities by a shared factor: a sure 3,000 against an 80 percent shot at 4,000 becomes a 25 percent shot at 3,000 against a 20 percent shot at 4,000, and preferences flip again. Both violate independence, so the difference is not which axiom breaks but which manipulation does the work: the common-consequence version alters a shared outcome, the common-ratio version alters shared odds, so each disciplines a different part of a theory and a model can fit one while missing the other. The practical lesson is narrow but real: an outcome both options deliver identically, which cancels on paper, still moves how people rank them, so making that shared branch salient can push someone from the safe choice to the aggressive one.
Examples
People prefer a sure $1M to a gamble that risks getting nothing; but once both options already carry a large chance of nothing, they flip to the riskier, higher-paying gamble.
A patient picks the operation with a certain modest recovery over a riskier one promising full mobility. Add the same large chance the disease returns regardless, and she flips to the riskier surgery.
A firm takes the guaranteed contract over the bigger speculative one. Point out that both depend on the same shaky client surviving the year, and it suddenly prefers the speculative deal.
A ward manager choosing between two risky staffing plans prefers the bolder one. Add a branch the plans share — under either, the ward keeps its teaching accreditation in almost every scenario — and the cautious plan becomes close to a sure thing, and she switches to it. The clause was added to both sides in identical form, so it should have cancelled.
A grants panel wants to know whether its members are chasing certainty or fleeing the zero. It reruns the choice with the guaranteed award trimmed to 99 percent, so nothing is certain any more but the empty branch stays where it was. If the pull toward the safe option survives, certainty was never what was doing the work.
First described in Maurice Allais (1953); analysis in Tversky & Kahneman (1979).
Key references
- Blavatskyy, P., Ortmann, A., & Panchenko, V. (2022). On the experimental robustness of the Allais paradox. American Economic Journal: Microeconomics, 14(1), 143-163. doi.org/10.1257/mic.20190153
- Incekara-Hafalir, E., Kim, E., & Stecher, J. D. (2021). Is the Allais paradox due to appeal of certainty or aversion to zero? Experimental Economics, 24(3), 751-771. doi.org/10.1007/s10683-020-09678-4
- Millroth, P., Nilsson, H., & Juslin, P. (2019). The decision paradoxes motivating Prospect Theory: The prevalence of the paradoxes increases with numerical ability. Judgment and Decision Making, 14(4), 513-533. doi.org/10.1017/S1930297500006161
- Huck, S., & Müller, W. (2012). Allais for all: Revisiting the paradox in a large representative sample. Journal of Risk and Uncertainty, 44(3), 261-293. doi.org/10.1007/s11166-012-9142-8
- Kahneman, D., & Tversky, A. (1979). Prospect theory: An analysis of decision under risk. Econometrica, 47(2), 263-291. doi.org/10.2307/1914185
- Allais, M. (1953). Le comportement de l'homme rationnel devant le risque: Critique des postulats et axiomes de l'école américaine. Econometrica, 21(4), 503-546. doi.org/10.2307/1907921