Justification for normalization in a ratio scale data

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Without loss of generality, I asked a group of participants $X=\{x_1,x_2,\ldots ,x_m\}$ to give scores in a $L$-point ratio scale $0,\ldots,l$ to different items $C=\{c_1,c_2,\ldots ,c_n\}$ based on the relative importance. They are asked to give at least $1$ item as highest score $l$, i.e., most important. Also, they can only select $y$ item as important, where $y\leq n. $ After they give scores to all items. I normalize scores of each participant, for one participant, the score of one item $c_i$ is calculated as follows:

$$s_{i,\textrm{normalized}}=\frac{s_i}{\sum_{j=1}^{n}{s_j}}.$$

I try to justify this step: The participants are required to give at least one item as highest scores, because I want to keep it in the same scale. However, the "most important" has different meaning to different participants. I normalize the score so that the problem is converted to "distribute $1$ to all items". By doing this step, we can distinguish the highest score $l$ from different participants. And the scores given by participants are consistent.

A simple example, three people give scores to three items in a $0,\ldots,5$ scale. A matrix can be gotten:

$$\begin{matrix}&\begin{matrix}a_1&a_2&a_3\\\end{matrix}\\\begin{matrix}c_1\\c_2\\c_3\\\end{matrix}&\left[\begin{matrix}5&3&5\\5&4&2\\5&5&3\\\end{matrix}\right]\\\end{matrix}$$

The normalized matrix is then:

$$\left[\begin{matrix}0.33&0.25&0.5\\0.33&0.33&0.2\\0.33&0.42&0.3\\\end{matrix}\right]$$

So the highest score of participants are different, $5$ given by $x_1$ has the same value as $4$ given by $x_2$, i.e., $0.33$.

I know it is quite a post-hoc question, but I still want to know if it can justify this normalization procedure.