Many impossibility results in mechanism design rely on the Revelation Principle, introduced by Roger Myerson in his foundational work on mechanism design (Myerson, 1979; 1981). Informally, the Revelation Principle states that for a broad class of mechanisms, any outcome that can be implemented through techniques that ask participants to take actions within the mechanism can also be implemented by a direct mechanism -- one in which participants simply report their preferences truthfully and the mechanism computes the outcome.
In situations where the Revelation Principle can be used, study of the direct mechanism often allows economists to prove the general impossibility of achieving certain outcomes involving efficiency, incentive compatibility, and welfare—optimality from the full mechanism. The limitation is important however as while mechanisms that are not convertible under the Revelation Principle are rare, they do exist and are not bound by impossibility results generated by it.
As such, given that the non-convertibility of Saito under the Revelation Principle is a valuable property of the mechanism, this page explains specifically why Saito operates outside the domain in which the Revelation Principle applies. Readers should note that the claim is not an argument that the Revelation Principle is incorrect, merely that its assumptions do not hold in the setting in which Saito operates, and that revelation-based reductions are not possible with routing mechanisms.
Non-convertibility in theory and practice is created by three informational properties of routing mechanisms: the endogeneity of time, costly action-in-mechanism, and infinite-sized preference maps.
Whereas in other mechanisms time is fixed by the mechanism in advance, in Saito the speed of block production and the rates at which time can be traded-off for other forms of utility depend on the choices and routing strategies made by all participants in the system. This makes time simultaneously:
While participants may form expectations about how various routing and bidding strategies affect their own speed-of-inclusion, the mechanism does not supply a stable, exogenous quantity of time that it can ask users to value as a common external reference. Instead:
This undermines the applicability of the Revelation Principle, as the Revelation Principle assumes users are reporting well-defined preferences for specific amounts of utility that must exist prior to their strategic interaction in the mechanism. When the supply of time and other forms of utility are manipulable endogenously by the mechanism in the way that Saito does, this assumption fails.
These limitations are well recognized in the mechanism design literature in seminal works discussing implementation in the presence of interdependent values (Maskin, 1992; Dasgupta and Maskin, 2000; Bergemann and Morris), dynamic mechanism design (Bergemann and Välimäki), and costly communication (Renou and Tomala). Saito operates in exactly this class of fluid environment where the assumptions required for the Revelation Principle do not hold.
In Saito, users do not communicate preferences by reporting them.
They indicate their comparative preferences for certain forms of utility over others by taking actions that exclude the possibility of making other choices.
This occurs specifically through the broadcast strategies that users make, which:
For example:
Distributing transactions publicly invites competition and faster inclusion, but sacrifices the ability to trade certain forms of collusion goods at the prevailing exchange rate that private broadcast imposes on those sets of time-dependent trades. Conversely, routing sacrifices speed for collusion utility.
Once a routing decision is made, the alternatives that were not chosen cannot be recovered or reported later. Strategies that a direct mechanism might observe to be dominated are no longer possible, as players cannot switch to prefer a form of utility they have excluded through their bidding and broadcast strategies. Preferences are therefore revealed through irreversible action, not declaration.
Further complicating matters is that some payoff-relevant information in Saito is valuable precisely because it is not revealed: the mechanism can observe the outcomes of activities (the existence of a specific transaction in a specific mempool) but not the intentions or strategic intent motivating this signal. And some of the most important information in Saito is only visible in its absence:
These absences shape outcomes but they leave no observable trace that a mechanism can condition on, and -- together with the problems above -- block the Revelation Principle from working, given its assumption that:
Saito Consensus violates all three of these requirements:
As a result, replacing routing with direct reporting necessarily changes the incentive structure of the network and the set of outcomes that any direct mechanism could find implementable, which breaks the equivalent of the direct mechanism required for the correct functioning of the Revelation Principle.
These failures are documented to invalidate revelation-based reduction in studies of constrained message spaces and costly communication (Renou and Tomala), in models where strategic actions precede or replace reporting (Maskin, 1992; Dasgupta and Maskin, 2000), and in the literature on limited observability and information design (Holmström; Green and Laffont; Bergemann and Morris) and broadcast privacy (Attar et al., 2025). The latter shows that indirect mechanisms exploiting privacy and partial observability can, in some cases, implement equilibria that are impossible to achieve with full and truthful revelation of all agents’ preferences.
In Saito users submit bids for a bundle of goods involving three main forms of interacting utility:
These three forms of utility are not quasilinear, can each be traded-off against another through a change in bidding or broadcast strategy. As such, participants technically need to reveal their "full preference maps" to any direct mechanism, covering any theoretically possible bundle of these three forms of utility.
This problem combines with the fact that time is a continuously variable dimension to create an infinite number of combinations of utility, and the need for the mechanism to analyse and order them. Applying the Revelation Principle consequently require participants to report preference maps which are:
Reduction is known to be impossible in settings in which preferences cannot be compactly expressed or reported without loss as in this situation. These difficulties are central to the literature on multi-dimensional screening and non-linear pricing (Rochet and Choné, 1998; Armstrong, 1996, 2016), and in the foundational work on the communication limits of mechanisms (Hurwicz, 1972; Mount and Reiter, 1974; Milgrom, 1981). Saito operates squarely in this class of informationally-explosive environments where preferences cannot be compactly expressed even in theory, pushing it outside the domain in which revelation-based arguments are possible.