When I was an undergraduate math major, one of my classes got our professor to discuss his dissertation. It involved supplying a missing link in a proof. He showed us how he connected the dots, reasoning forward from the last already proven step and backward from its conclusion.

Years later, a cartoon by Sidney Harris reminded me of that. It showed two professors at a blackboard, working on a proof. There were equations on the left side and the right side of the blackboard, with a substantial space in between. There, written in all caps, was “THEN A MIRACLE OCCURS.” And one of the professors commented, “I think you should be more explicit here in step two.”

Ever since seeing that cartoon, I have noticed how often the same thing happens in public policy. Someone who wants to (or is paid to) “prove” a position gets stymied by a gap in their argument, and so is forced to invoke a “then a miracle occurs” step, enabling their supposed “proof” to continue.

Such miracles smuggle in logical or factual errors, or else invoking them would have been unnecessary. And unfortunately, few people pay enough attention to recognize and expose these flaws, which are usually further defended by misdirecting discussion to the defensible steps that are not in question and ad hominem attacks on those who notice and object.

One example is unions’ frequently repeated “proof” of why they deserve credit for raising all workers’ wages. The critical step is their erroneous assertion that forcing up union members’ wages also forces other employers to raise wages to retain their workers. That step could only hold if such higher-paying union jobs were actually available to non-union workers, since employers need not outbid nonexistent options to retain employees.

Unfortunately, the opposite happens. By artificially forcing up the cost of hiring their workers, unions reduce the number of jobs offered by their employers, because consumers buy less of their output at the resulting higher prices. Therefore, since there are fewer union jobs available, non-union workers do not face improved alternatives in unions. Their alternatives worsen, as displaced workers are forced into non-union occupations, pushing down wages there. In fact, since the crucial step in their argument is the exact opposite of the truth, if the rest of their argument is true, it actually proves union wage hikes hurt other workers, over and above the higher costs they must bear as consumers.

Unions, however, ignore this fatal error and proceed to the conclusion that their “proof” is true. But false premises or mistaken leaps of logic do not create true conclusions, regardless of how frequently they are repeated.

Similar miracle steps are assumed in virtually all arguments for price controls, as illustrated by rent control and minimum wages.

Pro-rent control arguments assert that rent controls benefit renters by making them able to pay less for apartments. However, while lowering legally allowable rents (assuming that all the evasion mechanisms can be controlled) means renters would like to be able to purchase more housing, it does not mean they will be able to find additional housing at those prices. Lowered rental prices lead landlords to offer less housing, so prospective renters get less housing even though they want more. The actual result is the opposite of the result being “sold.” The fact that renters are harmed, is, however, disguised by the fact that attention is focused on current renters. They are already in their apartments and have protections against eviction, and so they gain from the lower rents without having to bear the costs of searching for housing. In contrast, those forced to bear the resulting costs are prospective future renters who are more likely to find “No Vacancy” signs than available apartments, and such costs are largely overlooked because they have not occurred yet.

Minimum wage advocates take a similar approach. They assert that minimum wages benefit low-skill workers by making them able to earn more for their efforts. However, forcing up the lowest legally allowable wage (assuming all the evasion mechanisms can be controlled) does not mean prospective workers will be able to find the jobs they desire at those wages. Mandated higher wages lead employers to offer fewer jobs. Again, the actual result is the opposite of the one being “sold.” The fact that many low-skill workers will be harmed, is, however, disguised by the fact that attention is focused on those low-skill workers who do keep their jobs, hours of work and working circumstances. In contrast, those forced to bear the most serious costs are those who will lose their jobs or face eroded working conditions and prospective future workers who will find fewer options, and such costs are largely overlooked because they have not occurred yet.

Protectionism advocates depend on similar miraculous steps. The higher domestic prices and incomes for the favored industries and their workers and wages allegedly provide both direct benefits and multiplier effects. But that conclusion only follows if one ignores their origins in greater costs to consumers, and the even larger multiplied negative consequences which follow from them.

What links these and other “then a miracle occurs” arguments for government meddling is that they assume that the consequences of scarcity (e.g., the laws of supply, demand and comparative advantage) can be reversed, simply because proponents want them to be. Proponents may be so committed to their policy conclusions (typically because they advance their own self-interest) that they go to great lengths to avoid careful thinking about the supposed miracles their arguments need. But such commitment to one’s own position does not create miracles where there are none to be had. And policies that cannot work without miracles cannot work, however often someone asserts they will.