**Jury Trilemma:**

1. No punishing juries for a decision not based on the law and evidence.

2. No double jeopardy.

3. No jury nullifiication.

A legal system can have any two of these but not all three.

***

Spinning numbers:

Spinning numbers:

Voter A: u = -1, v = 0, w = 1

Voter B: u = 0, v = 1, w = -1

Voter C: u = 1, v = -1, w = 0

Therefore this trilemma:

u < v ;

v < w ;

w < u

though all agree that the order is linear, within {-1,0,1}.

***

**1/3 of two things:**

Let x equal sqrt(u) when this is defined on the reals;

then x is 0 or 1 or nil (meaning not existing).

Similarly let y = sqrt(v) ; and z = sqrt(w) :

Voter A: x = nil, y = 0, z = 1

Voter B: x = 0, y = 1, z = nil

Voter C: x = 1, y = nil, z = 0

Unanimous:

{x,y,z} has two elements; 0, 1 and nil.

the three are distinct because one doesn't exist

Majorities:

x exists

y exists

z exists

x and y do not co-exist

y and z do not co-exist

z and x do not co-exist

x is not 0

x is not 1

x is 0 or 1

y is not 0

y is not 1

y is 0 or 1

z is not 0

z is not 1

z is 0 or 1

***

**2/3 of one thing:**

Let x = sqrt(u(1-u)), y = sqrt(v(1-v)), z = sqrt(w(1-w)), when these are defined in the reals.

Voter A: x = nil, y = 0, z = 0

Voter B: x = 0, y = 0, z = nil

Voter C: x = 0, y = nil, z = 0

Unanimous:

{x,y,z} has one element; 0 twice, and nil.

Majorities:

x exists

y exists

z exists

x and y do not co-exist

y and z do not co-exist

z and x do not co-exist

x = 0

y = 0

z = 0

x not = y

y not = z

z not = x

***

**1/3 of one thing:**

Let x = sqrt(u-1), y = sqrt(v-1), z = sqrt(w-1), when these are defined in the reals.

Voter A: x = nil, y = nil, z = 0

Voter B: x = nil, y = 0, z = nil

Voter C: x = 0, y = nil, z = nil

Unanimous:

{x,y,z} has one element; 0, and nil twice.

Majorities:

x does not exist and x is not 0

y does not exist and y is not 0

z does not exist and z is not 0

x or y exists and equals 0

y or z exists and equals 0

z or x exists and equals 0

x and y do not equally exist

y and z do not equally exist

z and x do not equally exist

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