Constraint with higher priority don't have effect.

[yihuang]

from kiwisolver import Solver, Variable
s = Solver()
w = Variable('w')
s.addConstraint((w==1) | 1001)
s.addConstraint((w==2) | 1002)
s.addConstraint((w==3) | 1003)
s.addConstraint((w==4) | 1004)
s.updateVariables()
s.dump()
print('value of w:', w.value())

Output:

Objective
---------
4008 + 2002 * e3 + 2004 * e5 + 2002 * e6 + 4 * e7 + 2008 * e8

Tableau
-------
v1 | 3 + 1 * e6 + -1 * e7
e2 | 2 + 1 * e3 + 1 * e6 + -1 * e7
e4 | 1 + 1 * e5 + 1 * e6 + -1 * e7
e9 | 1 + -1 * e6 + 1 * e7 + 1 * e8

Infeasible
----------

Variables
---------
w = v1

Edit Variables
--------------

Constraints
-----------
1 * w + -4 == 0  | strength = 1004
1 * w + -3 == 0  | strength = 1003
1 * w + -2 == 0  | strength = 1002
1 * w + -1 == 0  | strength = 1001


('value of w:', 3.0)

The value of w should be 4.0.

[sccolbert]

The value of w should not be 4. You have three constraints with weights that say w should be less than 4. The cumulative effect of those weights is such that they overpower the last weight. It should be noted that your weights are extremely close together. You need large variations in weights to establish one as dominant.

For reference, the default weights have the following values:

• strength.weak == strength.create(0, 0, 1) == 1
• strength.medium == strength.create(0, 1, 0) == 1000
• strength.strong == strength.create(1, 0, 0) == 1000000
• strength.required == strength.create(1000, 1000, 1000) = 1001001000

So you can see that the default weights have quite a large variation in value. This is what allows medium to always outweigh weak and strong to outweigh medium, etc.

You could certainly craft a large enough system of constraints where a huge number of medium constraints would outweigh a strong constraint, but that's an edge case that wasn't worth the performance hit of implementing lexicographic strength comparisons internally.