1) I cut a cake (the ‘reference cake’) into three unequal slices A, B and C, from largest to smallest (approx 60%, 35% and 5% respectively

2) Four other people cut similar cakes into three unequal slices A, B and C: the ‘comparison cakes’. They have enough information to ensure that each slice is reasonably close to, but not identical to, the percentages of the reference cake slices. For example, they may cut slice A somewhere in the range 58-62%.

3) The size of the slices of each cake are expressed as percentages of the whole, summing to 100% for each cake

I need to establish which of the four cut comparison cakes is, overall, most similar to the reference cake, comparing slices A, B, and C in terms of percentage slices.

Methods tried so far are:

1) Sum of absolute differences between slices A to C of the reference cake to the comparison cakes. The comparison cake with the smallest sum of absolute differences wins.

2) Square root of sum of (difference squared). This seems to always give the same winner and ranking as method 1.

I need to know if there is some more formal statistical test that can be used to establish this answer.