A special exchange is an instrument which government can use to subsidize trade in a commodity without subsidizing either buyers or sellers. It is therefore substantially free of moral hazard and market distortion.
In a market where there is too little profit to support a market maker trade often grinds to a halt. When the spread between buyers and sellers is too small, nobody can make a living providing the value-added services required for buyers and sellers to find each-other and transact business. These kinds of markets must exist: they are just below the threshold of profitability required for the free market to function.
To form a special exchange, government subsidizes or operates a market maker, who’s job it is to match buyers and sellers in the given commodity. This market maker’s effectiveness can be measured by the volume of transactions which pass through it. In the instances where these transactions are at least sometimes taxable, an estimate can be made of the cost or benefit to the public based on increased tax revenues.
The argument against special exchanges is that government may be facilitating trade between buyers and sellers of a marginal service, but preventing the formation of market makers in that space by acting as one. However, if the subsidy to market makers in the arena is structural (a bonus paid as a percentage of the value of transactions facilitated) this problem can be kept to a strict minimum.
Areas in which special exchanges might make sense: car sharing, trading unused industrial tooling capacity, personal services for the disabled and poor in general.
In general, the special exchange is a useful utility, like the feebate, which could be applied to a variety of policy objectives. The non-market distorting subsidy is something of a holy grail, and in some areas the special exchange provides that utility.