Two-Daughter Problem and Selection Effect

두 딸 문제와 선택 효과

  • Received : 2016.10.02
  • Accepted : 2016.10.18
  • Published : 2016.10.31

Abstract

If we learn that 'Mrs Lee has two children and at least one of them is a daughter', what is our credence that her two children are all girls? Obviously it is 1/3. By assuming some other obvious theses it seem to be argued that our credence is 1/2. Also by just supposing we learn trivial information about the future, it seem to be argued that we must change our credence 1/3 into 1/2. However all of these arguments are fallacious, cannot be sound. When using the conditionalization rule to evaluate conformation of a hypothesis by an evidence, or to estimate credence change by information intake, there are some points to keep in mind. We must examine whether relevant information was given through a random procedure or a biased procedure. If someone with full information releases to us particular partial information, an observation, a testimony, an evidence selected intentionally by him, which means the particular partial information was not given by chance, or was not given accidentally or naturally to us, then the conditionalization rule should be employed very cautiously or restrictedly.

'한 어머니 상금 씨가 낳은 두 아이 가운데 적어도 하나는 딸이다'라는 정보를 입수했을 때 '상금 씨의 두 아이가 모두 딸이다'를 우리는 얼마큼 믿을 수 있는가? 이 확률이 1/3이라는 것은 거의 분명해 보인다. 그런데 상금 씨가 '보미는 내 딸이다'라는 정보를 새로 더 알려줄 경우 많은 학자들은 우리의 확률이 1/3에서 1/2로 바뀌어야 한다고 말한다. 하지만 나는 그 확률이 여전히 1/3에 머물러야 한다고 주장한다. 증거와 가설의 지지 관계나 정보 유입과 확률 변화를 가늠하기 위해 조건화 규칙을 사용할 때 우리가 주의해야 할 점이 있다. 관련 정보 또는 증거가 어떤 절차를 거쳐 우리에게 주어졌는지를 따져보아야 한다. 해당 증거가 마구잡이로 주어졌다고 여길 수 없을 때는 조건화 규칙을 조심해서 사용해야 한다. 다시 말해 특정 관찰, 증언, 증거가 주어지도록 정보를 갖고 있는 누군가가 그 증거를 각별히 선택하지는 않았는지 잘 따져야 한다. 관련 정보 또는 증거가 우연히 주어지지 않고 그 정보를 이미 알고 있는 사람이 그 정보를 각별히 골라 우리에게 제공한 것이라면, 그 정보는 때때로 우리의 믿음직함을 바꿀 만한 정보가 되지 못한다.

Keywords

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