I came up with my ranking based on four other rankings based on what I am looking for in my future undergraduate institution. This ranking works for me and it will serve as a starting point in my college search and selection process. I thought I would share it with others, in case there are others on this site who value the same things as I do.
Here is my background to help you decide if you should completely ignore this ranking because it may not be relevant to you at all 
**Short profile **
I am a white female who will most probably be full pay because my parents make too much money to qualify for any need based aid. I am also a high stats applicant from a moderately sized competitive public school. I will most probably apply ED somewhere to maximize my chances of admission but have not decided where yet.
** My ideal school profile** I want to attend a moderately sized university which will provide a well rounded liberal arts education. The school’s academic profile is important to me, since my parents will be spending a lot of money on my education. I am primarily focusing on universities with a good balance between teaching and research. Teaching for the obvious reason and good research because I believe undergrads can indeed benefit from attending a strong research university, provided teaching at that university doesn’t take a back seat. So I would be interested in universities which have a strong record of both teaching and research. I also want my fellow students to be high achieving and academically gifted, because I think that will enhance my academic experience. Sports is not a big focus of mine, but I do want a well rounded college experience.
**I used the following rankings **
USNews - Raw score weighted at 50%
CWUR - Raw score weighted at 25%
- According to their website: The Center for World University Rankings (CWUR) publishes the only global university ranking that measures the quality of education and training of students as well as the prestige of the faculty members and the quality of their research without relying on surveys and university data submissions.*
ARWU - Raw score weighted at 10%
- According to their website: ARWU uses six objective indicators to rank world universities, including the number of alumni and staff winning Nobel Prizes and Fields Medals, number of highly cited researchers selected by Thomson Reuters, number of articles published in journals of Nature and Science, number of articles indexed in Science Citation Index - Expanded and Social Sciences Citation Index, and per capita performance of a university.*
RUR ranking - Raw score weighted at 15%
- According to their website: Their ranking is an overall university ranking which measures performance of world universities by 20 unique indicators and 4 dimension areas: teaching, research, international diversity, financial sustainability *
Based on the above choices, here is how my composite ranking rated the Universities
Rank    Name                    Scaled Score
1   Harvard University   99.00
2   Stanford University  94.14
3   Princeton University     92.78
4   MIT                          92.71
5   University of Chicago    91.55
6   Columbia University  91.16
7   Yale University          89.35
8   Caltech                      86.19
9   UPenn                    84.04
10  Cornell University   81.66
11  Johns Hopkins            81.48
12  UC, Berkeley             81.47
13  Duke University          79.56
14  Northwestern             79.02
15  UCLA                     75.05
16  WashU                    73.87
17  Dartmouth College    73.86
18  Brown University     72.46
19  Vanderbilt University    71.67
20  University of Michigan   71.45
21  Notre Dame           70.62
22  Rice University          70.53
23  University of Virginia   68.95
24  Emory University     68.21
25  USC                          67.69
26  CMU                          66.97
27  UNC Chapel Hill          66.67
28  Georgetown           66.32
29  Tufts University             65.94
30  New York University  65.65
31  UC, San Diego            65.58
32  Wisconsin–Madison  64.62
33  Univ of Washington   63.64
34  University of Illinois     62.63
35  Wake Forest          62.58
36  Univ Rochester           62.47
37  Boston University    61.44
38  Georgia Tech             61.40
39  Case Western            61.36
40  UC, Santa Barbara    60.69
41  UC, Davis                    60.62
42  UT Austin                    59.95
43  Ohio State University    59.32
44  University of Florida    59.23
45  UC, Irvine                   59.11
46  Boston College           58.67
47  Pennsylvania State     58.58
48  University of Miami  58.39
49  Brandeis University  58.21
50  Univ of Pittsburgh   58.19
51  Univ of Minnesota    57.66
52  William and Mary     57.58
53  Univ of Maryland         57.45
54  Purdue University    57.30
55  Tulane University    57.12
56  Rutgers University   56.74
57  Northeastern Univ    56.46
58  RPI                          56.42
59  George Washington    56.24
60  Lehigh University    54.34
61  UC, San Francisco    54.11
62  Texas A&M University     53.95
63  Univ of Colorado     53.03
64  University of Utah   49.86
65  University of Arizona    48.97