How Green Card Lottery year 2011 Winners was Chosen. DV Lottery 2012 First Drawing - Randomness. Another way to look on it.
According to Act 203(e)(2): "Immigrant visa numbers made available under subsection (c) (relating
to diversity immigrants) shall be issued to eligible qualified immigrants strictly in a random order
established by the Secretary of State for the fiscal year involved", visa numbers shall be issued to
eligible qualified immigrants strictly in a random order (See Appendix A, for text of Act 203).
If you have a group of people and you want to randomly select some of them, there are many
possible ways for doing this. Here we will explain the general common mechanics of a random
selection:
Selection
Selection of people can be implemented using many different procedures. No matter what
procedure is used and what are the detailed steps, conceptually , the selection process is always a
two step process: The first step is to sort all people inside a list and the second step is to pick some
of them from the list.
Randomness
In order to make the selection procedure random, randomness should be integrated into at least one
of the two steps of selection (steps explained under selection item above), i.e. Either the sorting of
the people inside a list should be random or the picking of the people from the list needs to be
random.
Random Selection
Based on the above explanations, there are two possible general solutions for randomly selecting x
people among a group of people: (A) list the people in a random way, then select x elements in any specific order (e.g. First x elements)
(B) list the people in any specific order (e.g. sorted by first name), then select x elements randomly
Both methods are identical in the sense of randomness, meaning that either method will select
people in a completely random way. In method (A), randomness is applied when adding the people
to the list and then any arbitrary part of the list is freely picked, while in method (B) people are
added to the list in an arbitrary order and then the randomness is applied when picking the people.
Note: Multiple random selection methods can be mixed to provide a combined random selection.
The combined random selection will be at least as good as the best random selection used.
DV Lottery Program Random Selection
Now we explain how the DV Lottery program maps into above methods for random selection.
The method usually being used for DV random selection is an implementation of method (B) above.
First, people have been added to a list with no specific order, then a random function has been used
to select the people.
The method which has unintentionally been used for DV 2012 is an implementation of method (A)
above. People have been ordered randomly based on their application time and then an arbitrary
subset has been selected.
See appendix B for definitions of randomness, random generators, types of random generators, and
how to test randomness.
See appendix D explaining why the order of the application submission time, is a random order.
Conclusion
As explained, there are many different possible procedures for implementing random selection.
Most of the methods are conceptually based on a two step procedure. Methods (A) and (B) for
random selection were explained. It was shown that usually method (B) has been used for the DV
program, while for DV 2012 method (A) has been applied. It was explained that both methods are
completely random and can be considered equivalent in the sense of randomness.
So either one can
be used interchangeably, without regards to the differences in the mechanics of implementation.
In conclusion, It is clear that the procedure applied for DV 2012 drawing is a valid random
procedure, completely satisfying the law requirements. So the DV 2012 results should be fully
reinstated.
Appendix A
Act 203 (c) (d) (e) (f) (g) (h)
(c) Diversity Immigrants. -
(1) In general. - Except as provided in paragraph (2), aliens subject to the worldwide level specified
in section 201 (e) for diversity immigrants shall be allotted visas each fiscal year as follows:
(A) Determination of preference immigration. - The Attorney General shall determine for the most
recent previous 5-fiscal-year period for which data are available, the total number of aliens who are
natives of each foreign state and who (i) were admitted or otherwise provided lawful permanent
resident status (other than under this subsection) and (ii) were subject to the numerical limitations of
section 201(a) (other than paragraph (3) thereof) or who were admitted or otherwise provided
lawful permanent resident status as an immediate relative or other alien described in section 201(b)
(2) .
(B) Identification of high-admission and low-admission regions and high-admission and lowadmission
states. - The Attorney General -
(i) shall identify -
(I) each region (each in this paragraph referred to as a "high- admission region") for which the total
of the numbers determined under subparagraph (A) for states in the region is greater than 1/6 of the
total of all such numbers, and
(II) each other region (each in this paragraph referred to as a "low- admission region"); and
(ii) shall identify -
(I) each foreign state for which the number determined under subparagraph (A) is greater than
50,000 (each such state in this paragraph referred to as a "high-admission state"), and
(II) each other foreign state (each such state in this paragraph referred to as a "low-admission
state").
(C) Determination of percentage of worldwide immigration attributable to high-admission regions. -
The Attorney General shall determine the percentage of the total of the numbers determined under
subparagraph (A) that are numbers for foreign states in high- admission regions.
(D) Determination of regional populations excluding high- admission states and ratios of
populations of regions within low-admission regions and high-admission regions. - The Attorney
General shall determine -
(i) based on available estimates for each region, the total population of each region not including the
population of any high-admission state;
(ii) for each low-admission region, the ratio of the population of the region determined under clause
(i) to the total of the populations determined under such clause for all the low-admission regions;
and (iii) for each high-admission region, the ratio of the population of the region determined under
clause (i) to the total of the populations determined under such clause for all the high-admission
regions.
(E) Distribution of visas. -
(i) No visas for natives of high-admission states.- The percentage of visas made available under this
paragraph to natives of a high- admission state is 0.
(ii) For low-admission states in low-admission regions. - Subject to clauses (iv) and (v), the
percentage of visas made available under this paragraph to natives (other than natives of a highadmission
state) in a low-admission region is the product of-
(I) the percentage determined under subparagraph (C), and
(II) the population ratio for that region determined under subparagraph (D)(ii).
(iii) For low-admission states in high-admission regions. - Subject to clauses (iv) and (v), the
percentage of visas made available under this paragraph to natives (other than natives of a highadmission
state) in a high-admission region is the product of -
(I) 100 percent minus the percentage determined under subparagraph (C), and
(II) the population ratio for that region determined under subparagraph (D)(iii).
(iv) Redistribution of unused visa numbers. - If the Secretary of State estimates that the number of
immigrant visas to be issued to natives in any region for a fiscal year under this paragraph is less
than the number of immigrant visas made available to such natives under this paragraph for the
fiscal year, subject to clause (v), the excess visa numbers shall be made available to natives (other
than natives of a high-admission state) of the other regions in proportion to the percentages
otherwise specified in clauses (ii) and (iii).
(v) Limitation on visas for natives of a single foreign state. - The percentage of visas made available
under this paragraph to natives of any single foreign state for any fiscal year shall not exceed 7
percent
.
(F) Region defined. - Only for purposes of administering the diversity program under this
subsection, Northern Ireland shall be treated as a separate foreign state, each colony or other
component or dependent area of a foreign state overseas from the foreign state shall be treated as
part of the foreign state, and the areas described in each of the following clauses shall be considered
to be a separate region:
(i) Africa.
(ii) Asia.
(iii) Europe.
(iv) North America (other than Mexico).
(v) Oceania.
(vi) South America, Mexico, Central America, and the Caribbean.
(2) Requirement of education or work experience. - An alien is not eligible for a visa under this
subsection unless the alien-
(A) has at least a high school education or its equivalent, or
(B) has, within 5 years of the date of application for a visa under this subsection, at least 2 years of
work experience in an occupation which requires at least 2 years of training or experience.
(3) Maintenance of information. - The Secretary of State shall maintain information on the age,
occupation, education level, and other relevant characteristics of immigrants issued visas under this
subsection.
(d) Treatment of Family Members. - A spouse or child as defined in subparagraph (A), (B), (C), (D),
or (E) of section 101(b)(1) shall, if not otherwise entitled to an immigrant status and the immediate
issuance of a visa under subsection (a), (b), or (c), be entitled to the same status, and the same order
of consideration provided in the respective subsection, if accompanying or following to join, the
spouse or parent.
(e) Order of Consideration. -
(1) Immigrant visas made available under subsection (a) or (b) shall be issued to eligible
immigrants in the order in which a petition in behalf of each such immigrant is filed with the
Attorney General (or in the case of special immigrants under section 101(a)(27)(D) , with the
Secretary of State) as provided in section 204(a) .
(2) Immigrant visa numbers made available under subsection (c) (relating to diversity immigrants)
shall be issued to eligible qualified immigrants strictly in a random order established by the
Secretary of State for the fiscal year involved.
(3) Waiting lists of applicants for visas under this section shall be maintained in accordance with
regulations prescribed by the Secretary of State.
(f) Authorization for Issuance. - In the case of any alien claiming in his application for an immigrant
visa to be described in section 201(b)(2) or in subsection (a), (b), or (c) of this section, the consular
officer shall not grant such status until he has been authorized to do so as provided by section 204 .
(g) Lists.- For purposes of carrying out the Secretary's responsibilities in the orderly administration
of this section, the Secretary of State may make reasonable estimates of the anticipated numbers of
visas to be issued during any quarter of any fiscal year within each of the categories under
subsections (a), (b), and (c) and to rely upon such estimates in authorizing the issuance of visas.
The Secretary of State shall terminate the registration of any alien who fails to apply for an immigrant
visa within one year following notification to the alien of the availability of such visa, but the
Secretary shall reinstate the registration of any such alien who establishes within 2 years following
the date of notification of the availability of such visa that such failure to apply was due to
circumstances beyond the alien's control.
3/ (h) RULES FOR DETERMINING WHETHER CERTAIN ALIENS ARE CHILDREN-
(1) IN GENERAL.-- For purposes of subsections (a)(2)(A) and (d), a determination of whether an
alien satisfies the age requirement in the matter preceding subparagraph (A) of section 101(b)(1)
shall be made using--
(A) the age of the alien on the date on which an immigrant visa number becomes available for such
alien (or, in the case of subsection (d), the date on which an immigrant visa number became
available for the alien's parent), but only if the alien has sought to acquire the status of an alien
lawfully admitted for permanent residence within one year of such availability; reduced by
(B) the number of days in the period during which the applicable petition described in paragraph (2)
was pending.
(2) PETITIONS DESCRIBED- The petition described in this paragraph is--
(A) with respect to a relationship described in subsection (a)(2)(A), a petition filed under section
204 for classification of an alien child under subsection (a)(2)(A); or
(B) with respect to an alien child who is a derivative beneficiary under subsection (d), a petition
filed under section 204 for classification of the alien's parent under subsection (a), (b), or (c).
(3) RETENTION OF PRIORITY DATE- If the age of an alien is determined under paragraph (1) to
be 21 years of age or older for the purposes of subsections (a)(2)(A) and (d), the alien's petition
shall automatically be converted to the appropriate category and the alien shall retain the original
priority date issued upon receipt of the original petition.
(4) 5/ APPLICATION TO SELF-PETITIONS- Paragraphs (1) through (3) shall apply to selfpetitioners
and derivatives of self-petitioners.
Appendix B
1) General Definitions of "Random" and "Order" as Words
Related meanings of "random" in an adjective form, as defined in:
(1.a) The American Heritage Dictionary
- Having no specific pattern, purpose, or objective: random movements. See synonyms at chance.
- Mathematics & Statistics. Of or relating to a type of circumstance or event that is described by a
probability distribution.
- Of or relating to an event in which all outcomes are equally likely, as in the testing of a blood
sample for the presence of a substance.
(1.b) Collins English Dictionary
- Lacking any definite plan or prearranged order; haphazard a random selection
- (Mathematics & Measurements / Statistics) Statistics
- Chosen without regard to any characteristics of the individual members of the population so that
each has an equal chance of being selected
(1.c) Dictionary.com
- Proceeding, made, or occurring without definite aim, reason, or pattern: the random selection of
numbers.
- Statistics . of or characterizing a process of selection in which each item of a set has an equal
probability of being chosen.
Related meanings of "order" in a noun form, as defined in:
(1.d) The American Heritage Dictionary
- A condition of logical or comprehensible arrangement among the separate elements of a group.
- A sequence or arrangement of successive things: changed the order of the files.
(1.e) Collins English Dictionary
- A state in which all components or elements are arranged logically, comprehensibly, or naturally
- An arrangement or disposition of things in succession; sequence alphabetical order
2) Specific Definitions of "Random" and "Random Order"
(2.a) Wikipedia:
Randomness has somewhat disparate meanings as used in several different fields. It also has
common meanings which may have loose connections with some of those more definite meanings.
The Oxford English Dictionary defines "random" thus:
Having no definite aim or purpose; not sent or guided in a particular direction; made, done,
occurring, etc., without method or conscious choice; haphazard.
Closely connected, therefore, with the concepts of chance, probability, and information entropy,
randomness implies a lack of predictability. Randomness is a concept of non-order or noncoherence
in a sequence of symbols or steps, such that there is no intelligible pattern or
combination.
The fields of mathematics, probability, and statistics use formal definitions of randomness. In
mathematics, a random variable is a way to assign a value to each possible outcome of an event. In
probability and statistics, a random process is a repeating process whose outcomes follow no
describable deterministic pattern, but follow a probability distribution, such that the relative
probability of the occurrence of each outcome can be approximated or calculated.
For example, the
rolling of a fair six-sided die in neutral conditions may be said to produce random results, because
one cannot know, before a roll, what number will show up. However, the probability of rolling any
one of the six rollable numbers can be calculated. The term is often used in statistics to
signify well-defined statistical properties, such as a lack of bias or correlation.
(2.b) Random.Org:
Random Number
When discussing single numbers, a random number is one that is
drawn from a set of possible values, each of which is equally
probable. In statistics, this is called a uniform distribution,
because the distribution of probabilities for each number is
uniform (i.e., the same) across the range of possible values.
For example, a good (unloaded) die has the probability 1/6 of
rolling a one, 1/6 of rolling a two and so on. Hence, the
probability of each of the six numbers coming up is exactly the
same, so we say any roll of our die has a uniform distribution.
Sequence of Random Numbers
When discussing a sequence of random numbers, each number drawn
must be statistically independent of the others. This means
that drawing one value doesn't make that value less likely to
occur again. This is exactly the case with our unloaded die: If
you roll a six, that doesn't mean the chance of rolling another six changes.
How to Generate Random Numbers
There are two main approaches to generating random numbers using a computer: Pseudo-Random
Number Generators (PRNGs) and True Random Number Generators (TRNGs).
(A) Pseudo-Random Number Generators (PRNGs)
Essentially, PRNGs are algorithms that use mathematical formulae or simply precalculated tables to
produce sequences of numbers that appear random.
PRNGs are deterministic, meaning that a given sequence of numbers can be reproduced at a later
date if the starting point in the sequence is known. PRNGs are typically also periodic, which means
that the sequence will eventually repeat itself. While periodicity is hardly ever a desirable
characteristic, modern PRNGs have a period that is so long that it can be ignored for most practical
purposes.
(B) True Random Number Generators (TRNGs)
In comparison with PRNGs, TRNGs extract randomness from physical phenomena and introduce it
into a computer. You can imagine this as a die connected to a computer, but typically people use a
physical phenomenon that is easier to connect to a computer than a die is. The physical
phenomenon can be very simple, like the little variations in somebody's mouse movements or in the
amount of time between keystrokes.
The characteristics of TRNGs are quite different from PRNGs. They are nondeterministic, meaning
that a given sequence of numbers cannot be reproduced, although the same sequence may of course
occur several times by chance. TRNGs have no period.
How To Test and Measure Randomness
it is hard to test whether a given sequence of numbers is random. The reason is that if your random
number generator (or your die) is good, each possible sequence of values (or die rolls) is equally
likely to appear. It is impossible to prove definitively whether a given sequence of numbers (and the
generator that produced it) is random. So, if it is impossible to definitively prove randomness, what
can we do instead? The pragmatic approach is to take many sequences of random numbers from a
given generator and subject them to a battery of statistical tests. As the sequences pass more of the
tests, the confidence in the randomness of the numbers increases and so does the confidence in the
generator.
However, because we expect some sequences to appear nonrandom (like the ten rolls of six on our
die), we should expect some of the sequences to fail at least some of the tests. However, if many
sequences fail the tests, we should be suspicious.
Here is a list including some of the possible Randomness tests from NIST suite:
•Frequency Test: Monobit
•Frequency Test: Block
•Runs Test
•Test for the Longest Runs of Ones in a Block
•Binary Matrix Rank Test
•Discrete Fourier Transform (Spectral Test)
•Non-Overlapping Template Matching Test
•Overlapping Template Matching Test
•Maurer's Universal Statistical Test
•Linear Complexity Test
•Serial Test
•Approximate Entropy Test
•Cumulative Sums Test
•Random Excursions Test
•Random Excursions Variant Test
Appendix C
More algorithmic definition of two methods of selecting some random people from a group of
people:
Assumptions:
We have a group of N people
We want to randomly select X people among the N people (X < N)
First Method:
a. Add all people to a list of size N, using any arbitrary order. Each person will be assigned the
index number of the place where that person has been added in the list.
b. Choose a random number generator that will generate numbers between 0 and N.
c. Run the generator to produces one index number. The person with this index number is selected.
d. repeat step c above for X times to select exactly X people from the list
Second Method:
a. Choose a random number generator.
b. Run the generator and assign one generated number to each person
c. add all people to a list of size N sorted by their assigned number. The person with smallest
number will be the first person in the list, and the person with the largest number will be the last
person in the list.
d. the first X person in the list will be the selected people.
Appendix D
Here we will show that application submission time is a random order by showing that it satisfies
the common definitions of random, as well as the specific formal definitions.
Satisfies the common definitions of random:
1. Having no specific pattern, purpose, or objective:
- It is obvious that the time of each application submitted by each applicant has no specific pattern,
purpose, or objective. Each person could have submitted his/her application at any time during the
application period. In general, there has been no relation between different applicants time of
submission. So the time of applications submissions are considered independent events.
2.Of or relating to an event in which all outcomes are equally likely:
- Since there has been no relation between different applicants time of submission, the time of
applications submissions are considered independent events. Therefore the likelihood of any
outcome will be equal.
3. Lacking any definite plan or prearranged order; haphazard:
- Time of applications submissions have not been based on any definite plan, or any prearranged
order. In fact they are completely independent events.
4. Chosen without regard to any characteristics of the individual members of the population so that
each has an equal chance of being selected:
- Application time is not related to any specific Characteristic of the applicants. Everybody had
equally the same chance to apply at any time during the registration period.
5. proceeding, made, or occurring without definite aim, reason, or pattern:
- There has been no definite aim or reason for using this application submission time based order, as
declared by DOS. Also there has not been any known definite reason, aim, or pattern for the
submission time of the applications.
6. Statistics . of or characterizing a process of selection in which each item of a set has an equal
probability of being chosen:
- Everybody have had equal probability to apply at any specific time during the registration period.
So every one have had equal probability to be among any subset of all applicants ordered by their
application submission time.
Satisfies the specific definitions of random:
As explained in Appendix B, the random generators can be a True Random Number Generator
(TRNG), or Pseudo-Random Number Generators (PRNG). TRNGs are the one's based on a
physical event like the application submission time of DV 2012 applicants, or it can be based on a
computer algorithm probably like the one's that have been used in previous DV Lottery drawings.
Note that, in general, TRNGs are a better random generators compared to PRNGs.
In Conclusion, as you see the application submission time satisfies all common definitions of
random, also satisfies the formal definition of random generators, and is a true random generator
which is in fact a better random generator.
References
1) http://www.uscis.gov/ilink/docView/SLB/HTML/SLB/0-0-0-1/0-0-0-29/0-0-0-1059/0-0-0-1135.html
2) http://www.thefreedictionary.com/random
3) The American Heritage® Dictionary of the English Language, Fourth Edition copyright ©2000 by
Houghton Mifflin Company. Updated in 2009. Published by Houghton Mifflin Company. All rights
reserved.
4) Collins English Dictionary – Complete and Unabridged © HarperCollins Publishers 1991, 1994,
1998, 2000, 2003
5) http://dictionary.reference.com/browse/random
6) http://www.random.org/
By Babak Nouri, 07/12/11
