Command blocks which are connected to the same redstone wire (or any redstone source), so all command block will be activated in the same tick as a high signal would be applied to wire, will be executed in a certain order.
Often it seems like the order follows the order in which the redstone would be updated, but a lot of other cases it is very inconsistent.

This especially affects commands which conditionally (with arguments) alter dummy objectives. For example a row of the following command blocks:

/scoreboard players set @a[score_Test=0,score_Test_min=0] Test 1
/scoreboard players set @a[score_Test=1,score_Test_min=1] Test 2
/scoreboard players set @a[score_Test=2,score_Test_min=2] Test 3
/scoreboard players set @a[score_Test=3,score_Test_min=3] Test 0

Sometimes multiple command blocks will get triggered since the previous executed command block will make sure that the next will meet his arguments. However the size of the groups in which multiple get executed successfully seems very inconsistent, see screen-shots. I repeatedly clicked the first, most left button. Clicking the most right button will most of the time only trigger one but occupationally it would trigger two at once.

How to duplicate: place a row of command blocks with comparators sticking out of them and type the following command in each of them:
"/scoreboard players set @a[score_Test=<i>,score_Test_min=<i>] Test <i+1>"
for i=1 to i=number-of-command-blocks and at the last command block replace the value of <i+1> by 1. Run a redstone wire on top all of them and power the wire from different positions multiple times after each other. (you would also have to create the objective Test: "/scoreboard objectives add Test dummy").