No. One of the other answers posted links to the last several decades of analytic efforts to do this "objectively" through calculation bit length, and Kolmogorov demonstrated that it is theoretically impossible to demonstrate that one has identified the minimum number of bits in a particular code, or language, or steps in a logic method, to do this comparison.
The failure of Kolmogorov and Solomonoff is just the latest in a century and a half of rationalists failure to evade Kant's Critique of Pure Reason by attempting to do rationalism in more and more "precise" terms.
The first of the most notable of these efforts was by Frege, whose project was eventually undone by a math error. Russell and Whitehead attempted to redo Frege's project with corrected math, but their work failed to close. One of their students, Godel, discovered why -- leading to Godel's Incompleteness theorem.
More recent and related failures, specifically in the computation of inductive inference: Popper attempted to refute Kuhn's inference that paradigm shifts in science were JUST sociological happenstance by developing a quantification measure to show science was increasingly more "true" to reality -- and Popper's methodology was itself shown to be logically invalid.
Lakatos, with his Research Programmes and their progressively and regressivity, provides the best answer yet to Quine's observation that theories are always underdetermined by evidence. But Lakatos then wanted to quantify progressivity and regressivity of Research Programmes, and HIS method to do so also was shown to be logically invalid.
Also, there have been recent concerns that the "objective" frequentist statistics used by science until this century are ad hoc and can at times be misleading or "hacked". Bayesian statistics have been promoted as a logically more valid alternative, but Bayesian statistics rely upon a JUDGEMENT call by the statistician, in the selection of a "prior" probability for a hypothesis to be true. Different priors yield different answers. So Bayesian statistics are NOT "objective", subjectivity is intrinsic to them.
This is all just a reprise, over and over again, that one cannot establish anything about a contingent world, using anything which is "necessary", which logic is presumed to be in the Analytic approach. Kant pushed analytics into a secondary role in empiricism and characterizing this world, which is intrinsically a judgment call.
Note also, that logic is pluralist. One will get different answers to these questions, depending on which logic system one is presuming. https://www.cambridge.org/core/journals/think/article/guide-to-logical-pluralism-for-nonlogicians/EDFDFA1C9EB65DB71848DABD6B12D877 Hence, the appeal to a presumes "One True Logic" is itself a logic error.
Aside on whether simplicity is useful in empiricism
Our liking for simple worldviews is well established. Humans throughout history have latched on to universalized claims about "theories of everything", them dogmatically asserted them in the face of contradicting evidence. The non-religious have noted this is a characteristic of a religious mindset. Sociologists have noted that religious dogmatism is just a subset of the broader human trait of inclination toward ideological dogmatism, of all kinds of ideologies. That we have an intrinsic attraction for simplicity, and for ideologies, are things we should be SUSPICIOUS of, rather than presume are actually determining about the nature of our world.
The very simplest model of our universe is that of self-delusion. That only ourselves exist, and all other events and actors are really just "in our heads". This model will always win out in a "Occam's Razor" contest. Note, however, it involves a key assumption: DELUSION is asserted in order to dismiss data and observations.
Science and empiricism's response has been that only models that actually fit all the observations and data, rather than dismissing them as delusion, should be considered in an Occam contest. Note however, that like Popper's and Lakatos' efforts to formalize how to do empiricism -- THIS general rule is also not universalizable. We KNOW that we are sometimes deluded, so SOMETIMES, we WILL need to dismiss data. Science has to apply pragmatic standards of judgement (IE not objective) as to when to do so. A good pragmatic standard is that a delusion claimant has a very strong burden of "proof" (empiricism cannot provide "proof", so rename as "burden of justification") for any dismissal of data.
Contrary to the simplicity inclinations we have, what we have discovered about our universe, is that it is almost UNIMAGINABLY complex. Nobody today can even understand all of one field of science -- all scientists need to highly specialize within a general field before they can do useful work. Therefore, none of us can integrate all knowledge about our universe.
Plus, it appears to be non-integrable. Science has abandoned the globally reductive model, in favor of a combination of reductionism, wholism, and pluralism. See section 5 of this SEP entry: https://plato.stanford.edu/entries/scientific-reduction/ Plus scientism, the claim that science is the only source of knowledge about our world, has been rejected by scientists themselves. Reject global reduction and scientism, and it is then IMPOSSIBLE to build a logically coherent worldview. Multiple independent reference frames, if all valid, will of necessity lead to contradictory conclusions.
Additionally, even our most reductive science, physics, is non-calculable. Quantum Mechanics is indeterministic. As is Newtonian mechanics. See this answer: Deterministic or stochastic universe?
If our world is non-reductive, and non-deterministic, it is non-calculable, and this violates a starting assumption behind Solomonoff's thinking.
Science, therefore, cannot support logical coherence or simplicity. The best simplicity can offer is a USEFUL standard for evaluating science claims. And simplicity has proven to be so subject to rationalization (I have had a multiverse advocate claim to me that multiverses are simpler than a single universe), that Popper proposed a far more useful standard: more predictively powerful, where predictive power is measured by the potential for falsifiability.