People who conduct themselves with a great deal of honesty and abstain from cheating or lying would be considered to have a considerable

amount of what?

Integrity

Explanation:

Integrity is the practice of being honest and having strong moral and ethical principles and values. Integrity is related to the truthfulness and accuracy of one's actions. If a person has integrity, it means he is true to himself and would do nothing that dishonors him.

So,

People who conduct themselves with a great deal of honesty and abstain  from cheating or lying would be considered to have a considerable  amount of integrity.