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Overview of methodsCertainly, there are a dime a dozen of methods for evaluating employees. (Please see below). With all confidence, no methods are more easy and global than our created methods.
| As an example which illustrates ordinary employee evaluation methods, please assume that you use employee evaluation forms like this, and please ask yourself candidly who evaluate employee whether such forms is effective from the viewpoints of time-consuming. What we mean are that such evaluation is nothing but one way evaluation by boss. In this case, it should be pointed out that even if subordinates evaluate their boss, that similarly is evaluation based on one-sided views. As the obvious conclusion leading from the very simple fact that only excellent humans can know who are excellent, what we are looking for should be reciprocal and comprehensive employee evaluation methods, and that should be evaluation between peers and evaluation between subordinates and boss, moreover it should be quantified. Please think about whether there are such calculation methods or not. For instance, please assume below relation between team members. (Arrows means high evaluation)
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We can quantify this relation as follows.
| X=Z | (Smith is highly evaluated by only Johnson.) | ||
| Y=1/2X | (Mille is highly evaluated by only Smith, and Smith evaluates two members) | ||
| Z=1/2X+Y | (Johnson is highly evaluated by Smith and Miller, and Smith evaluates two members) | ||
That is
| X : Y : Z = 2 : 1 :2 | or | 0.4 : 0.2 : 0.4 | or | 40% : 20% 40% |
In that meaning, the ratio is unique. (As for details, please read technical notes)
So, we can get unique employee evaluation rank.
We, Existenz. Co., Ltd, name it EER (Employee evaluation rank)!. Needless to say, total of EER is 1 !.
Please strongly keep in mind that though Johnson are highly evaluated by two humans, he is the same value as Smith. In other words, only excellent employee (= Johnson) can know who (= Smith) are excellent.
Such evaluation has become possible by our employee evaluation rank which we, Existenz. Co., Ltd, have developed.
For instance, you can know employee evaluation rank by following steps below.
Step 1Please distribute small blank paper to employees,
and provide direction that;
1. Write your name and department name
2.According to your impression and intuitiveness, to your knowledge, write the name who are excellent employees.
3. But, never write your own name.
4. You can write two or more names, and please write at least one name if possible.
[References examples]
| Your name | A |
| Division name | retail |
| Excellent employees who you think 1.Never write your own name. 2.Please write at least one name if possible. |
C D |
Step 2After collecting the results in your company, please make database table like this. And, when a employee think that other employee is excellent on employee performance, please enter 1.
(example: When Mr A evaluates Mr C and D as excellent employee, please enter 1 like this. When Mr C evaluates only Mr A as excellent employee, please enter 1 like this.)
A = please enter real name, nickname, number for identification, A.B.C.D.E etc.
| evaluaters | A |
B |
C |
D |
E |
A(=evaluaters) |
0 | 0 | 1 | 1 | 0 |
B(=evaluaters) |
0 | 0 | 1 | 1 | 1 |
C(=evaluaters) |
1 | 0 | 0 | 0 | 0 |
D(=evaluaters) |
1 | 1 | 1 | 0 | 1 |
E(=evaluaters) |
0 | 0 | 0 | 0 | 0 |
If it is all right for you to send original data, and if you think that it is time- consuming to make database table, please Email to us the collected results, we make database table.(As for detail, please view How to order)
Step 3Please send us database via our inquirly form or Email. (As for detail, please view How to order). We will send the results of calculation via Email.
Example of database
| evaluaters | Linda | John | Paul | Mark | David |
| Linda | 0 | 0 | 1 | 1 | 0 |
| John | 1 | 0 | 0 | 0 | 1 |
| Paul | 0 | 1 | 0 | 0 | 0 |
| Mark | 0 | 1 | 1 | 0 | 1 |
| David | 0 | 0 | 0 | 0 | 0 |
Technical notes1. First of all
To our regret, we can not release more detailed information of our methods for evaluating employees more than the below description on the internet . We would venture to say that our methods are based on graph theory, and please keep in mind that calculation methods is power methods. (Though the fact might be already known on the internet, the heart of Google's technique are based on graph theory. )
2. Eigenvector of employee evaluation
Mathematically speaking, calculation results is eigenvector of reciprocal evaluation between employees and the eigenvalue is 1 on definition.
*Let u be a subject of employee evaluation . (Example:Linda = u)
*Let Fu be the set of high evaluation from u. (Example:Linda
Paul and Mark)*Let Bu be the set of high evaluation into u. (Example:John
Linda)*Let Nu = |Fu| be the number of high evaluation from u. (Example:Linda
Paul and Mark, the number is 2.)*Let c be a normalization factor, that is, the total rank of all evaluation is constant.
| Notes: Please remember that all humans have good and bad points. So, normalization factor means distribution of a constant, which we may set 0.05. Moreover, distribution of a constant ensure convergence of calculation by power method. |
Let E(u) be "some vector over the subjects that corresponds to a source of evaluation rank" .
Employee Evaluation Rank = u is given by
R'(u) = c
R'(v) / Nv +cE(u)(N is the number of subjects of employee evaluation.)
3.Perron-Frobenius Theorem
Does unique eigenvector of employee evaluation rank exist as had been expected?
Fortunately, Perron-Frobenius Theorem teaches us that:
*r =
(A) is the Perron root, r > 0 and r 
(A).*The algebraic multiplicity of r is 1.
*There exists a positive x > 0 such that Ax = rx.
*There is a unique Perron vector such that:
*Ap = rp.
*p > 0.
*||p||1 = 1 (where ||p||1means the L1-Norm of the vector p)
*There are no other nonnegative eigenvectors for A except for positive multiples of p.
from Carl D Mayer, [Matrix analysis and applied linear argebra P661-, Perron-Frobenius theory]
