Reflection Piece #1
May’s Theorem Staring Upon Reasonable Doubt
May’s theorem states that the fulfillment of
universal domain, anonymity, neutrality and
positive responsiveness implies a majority rule,
furthermore, a majority rule implies the
fulfillment of these four principles. In this essay
I will navigate through possible rationale to
deviate from the majority rule by violating one
or more of the principles previously stated. To do
so, I will focus on the case of the unanimity rule
applied to reaching a verdict in criminal cases
(for a jury of twelve, all twelve jurors must vote
to convict for a guilty verdict to be the unique
outcome). First, I will discuss the ways in which
the rule violates neutrality, but follows universal
domain, positive responsiveness and anonymity;
and then I will introduce reasonable doubt and why it leads to a rational deviation from majority
rule.
For a rule to be neutral it must satisfy two conditions: in case of equal number of individuals
preferring a and b, the rule should specify ab and, if x number of individuals prefer a and y
individuals prefer b, the winning alternative in position (x,y) must be either the opposite of the
winning alternative of (y,x) or ab in both cases. This rule is easy to view graphically. The first
condition of the rule tells us that the anti-diagonal should be ab and that the graph should be
symmetrical along the anti-diagonal. Let’s go back to the unanimity rule in a twelve juror
situation. The graph above depicts the winning alternative under all preferences of jurors. It is
easy to see that this rule is not neutral as the anti-diagonal establishes an innocent verdict and it
is not symmetric with respect to the anti-diagonal. But what does this really mean? What the
graph is telling us is that ties will always lead to a winner (in this case innocent), and also, that if
we switch around the number of votes for both alternatives, the opposite alternative will not win
in all cases. For example when neutrality holds, if 7 jurors vote innocent, 5 vote guilty and the
verdict is innocent, when we flip the votes around, the verdict should also flip. So, if 7 jurors
vote guilty and 5 vote innocent, the verdict should be guilty, however, that is not the case. Now
that we have established that the unanimity rule violates neutrality let’s look at why the other
three properties hold.
Universal domain requires a rule to establish a definite outcome in every possible scenario of
individual preferences. Once again, it is easy to see this in the graph, as there is a clear winner
for every case of juror votes. In the case of the jury there are three possible options: a majority of
jurors vote guilty, a majority votes innocent or there are equal amounts of votes for both options.
The unanimity rule determines an alternative in all three cases. Unless all twelve jurors vote
guilty, the verdict will be innocent. Similarly anonymity is easy to analyze, as each juror is
treated equally and their names have no significance. If we shuffle the names and preferences
around, the graph will remain the same. Finally we must look at positive responsiveness.
Graphically this is also easy to see. To the south-east of all cases where the verdict is innocent,
the verdict is also innocent, and since there is nothing north-west of the only case where the
verdict is guilty the principle is satisfied. Thus, as votes increase in favor of the winning verdict,
innocent or guilty, (while the votes for the other alternative remain the same), the verdict will
still be the previous.
Finally, let’s see why there is rationality behind the violation of one of these principles. I believe
it is critical to first establish what constitutes a criminal case. This varies from state to state in the
United States. For purposes of this essay I will solely focus on New York City legislation. In new
York City, there can only be a jury for class “A” misdemeanors (the most serious type of
misdemeanor where punishment can be up to one year of jail) and felonies (most serious types of
crime including: murder, rape, robbery, arson etc, where punishments are of at least a year in jail
and up to life imprisonment). As you can see, the punishments in these types of cases are severe
and are not solely limited to the sentence itself. For example, a criminal record can impede you
from getting housing or a job. It is here where Blackstone’s Formulation comes into play.
William Blackstone was an English jurist who believed, “It is better that ten guilty persons
escape than that one innocent suffer”. He formulated that the punishments stated above are so
harmful that the protection of innocence is a priority. Here is born one of the most important
foundations of criminal law in the United States, “everyone is innocent until proven otherwise”.
During criminal cases in the United States, the prosecution must prove that the defendant is
guilty beyond “reasonable doubt” not the other way around . In case of reasonable doubt the
defendant must be allowed to walk free. It is important to highlight the difference between what
a juror believes happened and what they are certain happened, we must also take into account
that according to the sixth amendment of the Bill of Rights, the jury must be impartial. If there is
no sufficient evidence for a juror to be certain the defendant is guilty, there is still “reasonable
doubt”, or in other words, a possibility of convicting an innocent person which would be
somewhat a crime in of itself.
When first coming across Blackstone’s formulation I was ethically conflicted as I was unsure in
terms of looking at a society as a whole, if it is better to convict the innocent or to let the guilty
walk. However, I then looked at the issue from a legal perspective. The right of liberty is
repeatedly mentioned in important founding documents. The declaration of independence states,
“ that all men are created equal, that they are endowed by their Creator with certain unalienable
Rights, that among these are Life, Liberty and the pursuit of Happiness.”. The constitution of the
United States declares, “We the People of the United States, in Order to form a more perfect
Union, establish Justice, insure domestic Tranquility, provide for the common defense, promote
the general Welfare, and secure the Blessings of Liberty to ourselves and our Posterity, do ordain
and establish this Constitution for the United States of America.” The sixth amendment of the
Bill of Rights states, “nor shall any person be deprived .... of life, liberty, or property without due
process of law. ” In addition to the unanimity rule being an ethical discussion, it is also one of the
law. As shown above, this country was founded upon the idea that the government is present to
protect the unalienable rights mentioned in the constitution, including liberty. Applying the
unanimity rule to the criminal cases discussed in the previous paragraph ensures that the supreme
law of this country is followed. In addition, to think of changing the rule, implies the plausibility
of an innocent person’s rights being violated, and is going against the institutions of this country.
In both theory and practice, the unanimity rule is the most secure way to protect innocent people
and ensure the realization of the United States constitution.
I feel we have no choice to conclude that the unanimity rule is the only rule that ensures a
society’s rights are fully safeguarded, and is also the one that is most cemented in the laws that
this specific society has been abiding by since 1787. The violation of the neutrality rule, in this
case, is substantiated by just one innocent person. The presence of disagreement among a jury is
not sufficient to crumble an innocent person’s life to pieces, thus, May’s theorem fails when
being pitted against one of our most important rights, liberty.